ERF_ComputeTurbulentViscosity.cpp File Reference

#include "ERF_SurfaceLayer.H"
#include "ERF_EddyViscosity.H"
#include "ERF_Diffusion.H"
#include "ERF_PBLModels.H"
#include "ERF_TileNoZ.H"
#include "ERF_TerrainMetrics.H"
#include "ERF_MoistUtils.H"
#include "ERF_RichardsonNumber.H"

Include dependency graph for ERF_ComputeTurbulentViscosity.cpp:

Functions
void	ComputeTurbulentViscosityLES (Vector< std::unique_ptr< MultiFab >> &Tau_lev, const MultiFab &cons_in, MultiFab &eddyViscosity, MultiFab &Hfx1, MultiFab &Hfx2, MultiFab &Hfx3, MultiFab &Diss, const Geometry &geom, bool use_terrain_fitted_coords, Vector< std::unique_ptr< MultiFab >> &mapfac, const std::unique_ptr< MultiFab > &z_phys_nd, const TurbChoice &turbChoice, const Real const_grav, std::unique_ptr< SurfaceLayer > &, const MoistureComponentIndices &moisture_indices, const MultiFab *xvel, const MultiFab *yvel)
void	ComputeTurbulentViscosityLES_EB (Vector< std::unique_ptr< MultiFab >> &Tau_lev, const MultiFab &cons_in, MultiFab &eddyViscosity, MultiFab &Hfx1, MultiFab &Hfx2, MultiFab &Hfx3, const Geometry &geom, Vector< std::unique_ptr< MultiFab >> &mapfac, const TurbChoice &turbChoice, const Real const_grav, [[maybe_unused]] const SolverChoice &solverChoice, std::unique_ptr< SurfaceLayer > &, const MoistureComponentIndices &moisture_indices, const eb_ &ebfact, const MultiFab *xvel, const MultiFab *yvel)
void	ComputeTurbulentViscosityRANS (Vector< std::unique_ptr< MultiFab >> &, const MultiFab &cons_in, const MultiFab &wdist, MultiFab &eddyViscosity, MultiFab &Hfx1, MultiFab &Hfx2, MultiFab &Hfx3, MultiFab &Diss, const Geometry &geom, bool use_terrain_fitted_coords, Vector< std::unique_ptr< MultiFab >> &, const std::unique_ptr< MultiFab > &z_phys_nd, const TurbChoice &turbChoice, const Real const_grav, std::unique_ptr< SurfaceLayer > &SurfLayer, const MultiFab *z_0)
void	ComputeTurbulentViscosity (double dt, const MultiFab &xvel, const MultiFab &yvel, Vector< std::unique_ptr< MultiFab >> &Tau_lev, MultiFab &cons_in, const MultiFab &wdist, MultiFab &eddyViscosity, MultiFab &Hfx1, MultiFab &Hfx2, MultiFab &Hfx3, MultiFab &Diss, const Geometry &geom, Vector< std::unique_ptr< MultiFab >> &mapfac, const std::unique_ptr< MultiFab > &z_phys_nd, const std::unique_ptr< MultiFab > &z_phys_cc, const SolverChoice &solverChoice, std::unique_ptr< SurfaceLayer > &SurfLayer, const MultiFab *z_0, const bool &use_terrain_fitted_coords, const bool &use_moisture, int level, const BCRec *bc_ptr, const eb_ &ebfact, bool vert_only, const MultiFab *qheating_rates)

Function Documentation

ComputeTurbulentViscosity()

void ComputeTurbulentViscosity	(	double	dt,
		const MultiFab &	xvel,
		const MultiFab &	yvel,
		Vector< std::unique_ptr< MultiFab >> &	Tau_lev,
		MultiFab &	cons_in,
		const MultiFab &	wdist,
		MultiFab &	eddyViscosity,
		MultiFab &	Hfx1,
		MultiFab &	Hfx2,
		MultiFab &	Hfx3,
		MultiFab &	Diss,
		const Geometry &	geom,
		Vector< std::unique_ptr< MultiFab >> &	mapfac,
		const std::unique_ptr< MultiFab > &	z_phys_nd,
		const std::unique_ptr< MultiFab > &	z_phys_cc,
		const SolverChoice &	solverChoice,
		std::unique_ptr< SurfaceLayer > &	SurfLayer,
		const MultiFab *	z_0,
		const bool &	use_terrain_fitted_coords,
		const bool &	use_moisture,
		int	level,
		const BCRec *	bc_ptr,
		const eb_ &	ebfact,
		bool	vert_only,
		const MultiFab *	qheating_rates
	)

Wrapper to compute turbulent viscosity with LES or PBL.

Parameters

[in]	dt	time step
[in]	xvel	velocity in x-dir
[in]	yvel	velocity in y-dir
[in]	Tau_lev	strain at this level
[in]	cons_in	cell center conserved quantities
[in]	wdist	wall distance
[out]	eddyViscosity	turbulent viscosity
[out]	Hfx1	heat flux in x-dir
[out]	Hfx2	heat flux in y-dir
[out]	Hfx3	heat flux in z-dir
[out]	Diss	dissipation of turbulent kinetic energy
[in]	geom	problem geometry
[in]	mapfac	map factors
[in]	z_phys_nd	nodal physical z coordinates
[in]	z_phys_cc	cell-centered physical z coordinates
[in]	solverChoice	container with solver, diffusion, and turbulence parameters
[in]	SurfLayer	optional surface-layer model
[in]	z_0	roughness length
[in]	use_terrain_fitted_coords	flag for terrain-fitted coordinates
[in]	use_moisture	flag for moisture physics
[in]	level	AMR level
[in]	bc_ptr	boundary condition records
[in]	ebfact	EB factories for cell- and face-centered variables
[in]	vert_only	flag for vertical components of eddyViscosity
[in]	qheating_rates	radiation heating rates (SW, LW components)

{
    BL_PROFILE_VAR("ComputeTurbulentViscosity()",ComputeTurbulentViscosity);
    //
    // In LES mode, the turbulent viscosity is isotropic (unless mix_isotropic is set to false), so
    // the LES model sets both horizontal and vertical viscosities
    //
    // In PBL mode, the primary purpose of the PBL model is to control vertical transport, so the PBL model sets the vertical viscosity.
    // Optionally, the PBL model can be run in conjunction with an LES model that sets the horizontal viscosity
    // (this isn’t truly LES, but the model form is the same as Smagorinsky).
    //
    // ComputeTurbulentViscosityLES populates the LES viscosity for both horizontal and vertical components.
    // ComputeTurbulentViscosityPBL computes the PBL viscosity just for the vertical component.
    //
 
    TurbChoice turbChoice = solverChoice.turbChoice[level];
    const Real const_grav = solverChoice.gravity;
 
    if (!SurfLayer) {
        AMREX_ALWAYS_ASSERT(!vert_only);
    }
 
    bool impose_phys_bcs = true;
 
    if (turbChoice.les_type != LESType::None) {
        if (solverChoice.terrain_type == TerrainType::EB) {
            ComputeTurbulentViscosityLES_EB(Tau_lev,
                                        cons_in, eddyViscosity,
                                        Hfx1, Hfx2, Hfx3,
                                        geom,
                                        mapfac, turbChoice, const_grav,
                                        solverChoice,
                                        SurfLayer, solverChoice.moisture_indices,
                                        ebfact, &xvel, &yvel);
        } else {
            ComputeTurbulentViscosityLES(Tau_lev,
                                        cons_in, eddyViscosity,
                                        Hfx1, Hfx2, Hfx3, Diss,
                                        geom, use_terrain_fitted_coords,
                                        mapfac, z_phys_nd, turbChoice, const_grav,
                                        SurfLayer, solverChoice.moisture_indices,
                                        &xvel, &yvel);
        }
    }
 
    if (turbChoice.rans_type != RANSType::None) {
        ComputeTurbulentViscosityRANS(Tau_lev,
                                      cons_in, wdist,
                                      eddyViscosity,
                                      Hfx1, Hfx2, Hfx3, Diss,
                                      geom, use_terrain_fitted_coords,
                                      mapfac, z_phys_nd, turbChoice, const_grav,
                                      SurfLayer, z_0);
    }
 
    if (turbChoice.pbl_type == PBLType::MYJ) {
        ComputeDiffusivityMYJ(dt, xvel, yvel, cons_in, eddyViscosity,
                              geom, turbChoice, SurfLayer,
                              use_terrain_fitted_coords, use_moisture,
                              level, bc_ptr, vert_only, z_phys_nd, z_phys_cc,
                              solverChoice.moisture_indices);
    } else if (turbChoice.pbl_type == PBLType::MYNN25) {
        ComputeDiffusivityMYNN25(xvel, yvel, cons_in, eddyViscosity,
                                 geom, turbChoice, SurfLayer,
                                 use_terrain_fitted_coords, use_moisture,
                                 level, bc_ptr, vert_only, z_phys_nd, z_phys_cc,
                                 solverChoice.moisture_indices);
    } else if (turbChoice.pbl_type == PBLType::MYNNEDMF) {
        ComputeDiffusivityMYNNEDMF(xvel, yvel, cons_in, eddyViscosity,
                                   geom, turbChoice, SurfLayer,
                                   use_terrain_fitted_coords, use_moisture,
                                   level, bc_ptr, vert_only, z_phys_nd, z_phys_cc,
                                   solverChoice.moisture_indices);
    } else if (turbChoice.pbl_type == PBLType::YSU) {
        ComputeDiffusivityYSU(xvel, yvel, cons_in, eddyViscosity,
                              geom, turbChoice, SurfLayer,
                              use_terrain_fitted_coords, use_moisture,
                              level, bc_ptr, vert_only, z_phys_nd, z_phys_cc,
                              solverChoice.moisture_indices);
    } else if (turbChoice.pbl_type == PBLType::MRF) {
        ComputeDiffusivityMRF(xvel, yvel, cons_in, eddyViscosity,
                              geom, turbChoice, SurfLayer,
                              use_terrain_fitted_coords, use_moisture,
                              level, bc_ptr, vert_only, z_phys_nd, z_phys_cc,
                              solverChoice.moisture_indices);
    } else if (turbChoice.pbl_type == PBLType::YSUNew) {
        ComputeDiffusivityYSUNew(xvel, yvel, cons_in, eddyViscosity,
                                 geom, turbChoice, SurfLayer,
                                 use_terrain_fitted_coords, use_moisture,
                                 level, bc_ptr, vert_only, z_phys_nd, z_phys_cc,
                                 solverChoice.moisture_indices,
                                 qheating_rates);
    } else if (turbChoice.uses_shoc_family()) {
        // NOTE: Nothing to do here. The SHOC class handles setting the vertical
        //       components of eddyDiffs in slow RHS pre.
    }
 
    //
    // At all levels we need to fill values outside the physical boundary for the LES coeffs.
    // In addition, for all cases, if at level > 0, we want to fill fine ghost cell values that
    // overlie coarse grid cells (and that are not in another fine valid region) with
    // extrapolated values from the interior, rather than interpolating from the coarser level,
    // since we may be using a different turbulence model there.
    //
    // Note: here "covered" refers to "covered by valid region of another grid at this level"
    // Note: here "physbnd" refers to "cells outside the domain if not periodic"
    // Note: here "interior" refers to "valid cells, i.e. inside 'my' grid"
    //
    {
        int is_covered    = 0;
        int is_notcovered = 1;
        int is_physbnd    = 2;
        int is_interior   = 3;
        iMultiFab cc_mask(eddyViscosity.boxArray(),eddyViscosity.DistributionMap(),1,1);
        cc_mask.BuildMask(geom.Domain(), geom.periodicity(), is_covered, is_notcovered, is_physbnd, is_interior);
 
        Box domain = geom.Domain();
        for (int i = 0; i < AMREX_SPACEDIM; ++i) {
            if (geom.isPeriodic(i)) {
                domain.grow(i,1);
            }
        }
 
        eddyViscosity.FillBoundary(geom.periodicity());
 
        int ncomp  = eddyViscosity.nComp();
 
#ifdef _OPENMP
#pragma omp parallel if (Gpu::notInLaunchRegion())
#endif
        for (MFIter mfi(eddyViscosity); mfi.isValid(); ++mfi)
        {
            Box vbx = mfi.validbox();
 
            Box planex_lo = mfi.growntilebox(1); planex_lo.setBig(0, vbx.smallEnd(0)-1);
            Box planey_lo = mfi.growntilebox(1); planey_lo.setBig(1, vbx.smallEnd(1)-1);
            Box planez_lo = mfi.growntilebox(1); planez_lo.setBig(2, vbx.smallEnd(2)-1);
 
            Box planex_hi = mfi.growntilebox(1); planex_hi.setSmall(0, vbx.bigEnd(0)+1);
            Box planey_hi = mfi.growntilebox(1); planey_hi.setSmall(1, vbx.bigEnd(1)+1);
            Box planez_hi = mfi.growntilebox(1); planez_hi.setSmall(2, vbx.bigEnd(2)+1);
 
            int i_lo   = vbx.smallEnd(0); int i_hi = vbx.bigEnd(0);
            int j_lo   = vbx.smallEnd(1); int j_hi = vbx.bigEnd(1);
            int k_lo   = vbx.smallEnd(2); int k_hi = vbx.bigEnd(2);
 
            const Array4<Real>& mu_turb = eddyViscosity.array(mfi);
            const Array4<int>& mask_arr = cc_mask.array(mfi);
 
            auto domlo = lbound(domain);
            auto domhi = ubound(domain);
 
            ParallelFor(planex_lo, [=] AMREX_GPU_DEVICE (int i, int j, int k) noexcept
            {
                int lj = amrex::min(amrex::max(j, domlo.y), domhi.y);
                int lk = amrex::min(amrex::max(k, domlo.z), domhi.z);
                if ((mask_arr(i,j,k) == is_notcovered && mask_arr(i_lo,lj,lk) != is_notcovered) ||
                    (mask_arr(i,j,k) == is_physbnd    && i < domlo.x && impose_phys_bcs)) {
                    for (int n = 0; n < ncomp; n++) {
                        mu_turb(i,j,k,n) = mu_turb(i_lo,lj,lk,n);
                    }
                }
            });
            ParallelFor(planex_hi, [=] AMREX_GPU_DEVICE (int i, int j, int k) noexcept
            {
                int lj = amrex::min(amrex::max(j, domlo.y), domhi.y);
                int lk = amrex::min(amrex::max(k, domlo.z), domhi.z);
                if ((mask_arr(i,j,k) == is_notcovered && mask_arr(i_hi,lj,lk) != is_notcovered) ||
                    (mask_arr(i,j,k) == is_physbnd    && i > domhi.x && impose_phys_bcs)) {
                    for (int n = 0; n < ncomp; n++) {
                        mu_turb(i,j,k,n) = mu_turb(i_hi,lj,lk,n);
                    }
                }
            });
            ParallelFor(planey_lo, [=] AMREX_GPU_DEVICE (int i, int j, int k) noexcept
            {
                int lk = amrex::min(amrex::max(k, domlo.z), domhi.z);
                if ((mask_arr(i,j,k) == is_notcovered && mask_arr(i,j_lo,lk) != is_notcovered) ||
                    (mask_arr(i,j,k) == is_physbnd    && j < domlo.y && impose_phys_bcs)) {
                    for (int n = 0; n < ncomp; n++) {
                        mu_turb(i,j,k,n) = mu_turb(i,j_lo,lk,n);
                    }
                }
            });
            ParallelFor(planey_hi, [=] AMREX_GPU_DEVICE (int i, int j, int k) noexcept
            {
                int lk = amrex::min(amrex::max(k, domlo.z), domhi.z);
                if ((mask_arr(i,j,k) == is_notcovered && mask_arr(i,j_hi,lk) != is_notcovered)||
                    (mask_arr(i,j,k) == is_physbnd    && j > domhi.y && impose_phys_bcs)) {
                    for (int n = 0; n < ncomp; n++) {
                        mu_turb(i,j,k,n) = mu_turb(i,j_hi,lk,n);
                    }
                }
            });
            ParallelFor(planez_lo, [=] AMREX_GPU_DEVICE (int i, int j, int k) noexcept
            {
                if ((mask_arr(i,j,k) == is_notcovered && mask_arr(i,j,k_lo) != is_notcovered) ||
                    (mask_arr(i,j,k) == is_physbnd    && k < domlo.z && impose_phys_bcs)) {
                    for (int n = 0; n < ncomp; n++) {
                        mu_turb(i,j,k,n) = mu_turb(i,j,k_lo,n);
                    }
                }
            });
            ParallelFor(planez_hi, [=] AMREX_GPU_DEVICE (int i, int j, int k) noexcept
            {
                if ((mask_arr(i,j,k) == is_notcovered && mask_arr(i,j,k_hi) != is_notcovered) ||
                    (mask_arr(i,j,k) == is_physbnd    && k > domhi.z && impose_phys_bcs)) {
                    for (int n = 0; n < ncomp; n++) {
                        mu_turb(i,j,k,n) = mu_turb(i,j,k_hi,n);
                    }
                }
            });
        } // mfi
 
        eddyViscosity.FillBoundary(geom.periodicity());
    }
}

Referenced by ERF::advance_dycore().

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ComputeTurbulentViscosityLES()

void ComputeTurbulentViscosityLES	(	Vector< std::unique_ptr< MultiFab >> &	Tau_lev,
		const MultiFab &	cons_in,
		MultiFab &	eddyViscosity,
		MultiFab &	Hfx1,
		MultiFab &	Hfx2,
		MultiFab &	Hfx3,
		MultiFab &	Diss,
		const Geometry &	geom,
		bool	use_terrain_fitted_coords,
		Vector< std::unique_ptr< MultiFab >> &	mapfac,
		const std::unique_ptr< MultiFab > &	z_phys_nd,
		const TurbChoice &	turbChoice,
		const Real	const_grav,
		std::unique_ptr< SurfaceLayer > &	,
		const MoistureComponentIndices &	moisture_indices,
		const MultiFab *	xvel,
		const MultiFab *	yvel
	)

Function for computing the turbulent viscosity with LES.

Parameters

[in]	Tau_lev	strain at this level
[in]	cons_in	cell center conserved quantities
[out]	eddyViscosity	turbulent viscosity
[out]	Hfx1	heat flux in x-dir
[out]	Hfx2	heat flux in y-dir
[out]	Hfx3	heat flux in z-dir
[out]	Diss	dissipation of turbulent kinetic energy
[in]	geom	problem geometry
[in]	use_terrain_fitted_coords	flag for terrain-fitted coordinates
[in]	mapfac	map factors
[in]	z_phys_nd	nodal physical z coordinates
[in]	turbChoice	container with turbulence parameters
[in]	const_grav	gravitational acceleration
[in]	moisture_indices	moisture component indices
[in]	xvel	x-direction velocity (for moist Ri correction)
[in]	yvel	y-direction velocity (for moist Ri correction)

{
    const GpuArray<Real, AMREX_SPACEDIM> cellSizeInv = geom.InvCellSizeArray();
    const Box& domain = geom.Domain();
 
    Real inv_Pr_t    = turbChoice.Pr_t_inv;
    Real inv_Sc_t    = turbChoice.Sc_t_inv;
    Real inv_sigma_k = one / turbChoice.sigma_k;
 
    bool use_thetav_grad = (turbChoice.strat_type == StratType::thetav);
    bool use_thetal_grad = (turbChoice.strat_type == StratType::thetal);
 
    bool isotropic = turbChoice.mix_isotropic;
 
    // SMAGORINSKY: Fill Kturb for momentum in horizontal and vertical
    //***********************************************************************************
    if (turbChoice.les_type == LESType::Smagorinsky)
    {
        Real Cs = turbChoice.Cs;
        bool smag2d = turbChoice.smag2d;
 
        // Define variables required inside device lambdas (scalars only)
        Real l_abs_g = const_grav;
        Real l_Ri_crit = turbChoice.Ri_crit;
        bool l_use_Ri_corr = turbChoice.use_Ri_correction;
        bool l_has_xvel = (xvel != nullptr);
        bool l_has_yvel = (yvel != nullptr);
 
#ifdef _OPENMP
#pragma omp parallel if (Gpu::notInLaunchRegion())
#endif
        for (MFIter mfi(eddyViscosity,TilingIfNotGPU()); mfi.isValid(); ++mfi)
        {
            Box bxcc  = mfi.growntilebox(1) & domain;
            const Array4<Real>& mu_turb = eddyViscosity.array(mfi);
            const Array4<Real>& hfx_x   = Hfx1.array(mfi);
            const Array4<Real>& hfx_y   = Hfx2.array(mfi);
            const Array4<Real>& hfx_z   = Hfx3.array(mfi);
            const Array4<Real const >& cell_data = cons_in.array(mfi);
            Array4<Real const> tau11 = Tau_lev[TauType::tau11]->array(mfi);
            Array4<Real const> tau22 = Tau_lev[TauType::tau22]->array(mfi);
            Array4<Real const> tau33 = Tau_lev[TauType::tau33]->array(mfi);
            Array4<Real const> tau12 = Tau_lev[TauType::tau12]->array(mfi);
            Array4<Real const> tau13 = Tau_lev[TauType::tau13]->array(mfi);
            Array4<Real const> tau23 = Tau_lev[TauType::tau23]->array(mfi);
            Array4<Real const> mf_u = mapfac[MapFacType::u_x]->const_array(mfi);
            Array4<Real const> mf_v = mapfac[MapFacType::v_y]->const_array(mfi);
            Array4<Real const> z_nd_arr = z_phys_nd->const_array(mfi);
 
            Array4<Real const> u_arr = (l_has_xvel) ? xvel->const_array(mfi) : Array4<Real const>{};
            Array4<Real const> v_arr = (l_has_yvel) ? yvel->const_array(mfi) : Array4<Real const>{};
 
            ParallelFor(bxcc, [=] AMREX_GPU_DEVICE (int i, int j, int k) noexcept
            {
                // =====================================================================
                // one STRAIN RATE MAGNITUDE CALCULATION
                // =====================================================================
                Real SmnSmn;
                if (smag2d) {
                    SmnSmn = ComputeSmnSmn2D(i,j,k,tau11,tau22,tau12);
                } else {
                    SmnSmn = ComputeSmnSmn(i,j,k,tau11,tau22,tau33,tau12,tau13,tau23);
                }
                Real strain_rate_magnitude = std::sqrt(two * SmnSmn);
 
                // =====================================================================
                // two GRID SCALE CALCULATION (filter width Δ)
                // =====================================================================
                Real dxInv = cellSizeInv[0];
                Real dyInv = cellSizeInv[1];
                Real dzInv = cellSizeInv[2];
                if (use_terrain_fitted_coords) {
                    dzInv /= Compute_h_zeta_AtCellCenter(i,j,k, cellSizeInv, z_nd_arr);
                }
 
                Real Delta;
                Real DeltaH;
                if (isotropic) {
                    Real cellVolMsf = one / (dxInv * mf_u(i,j,0) * dyInv * mf_v(i,j,0) * dzInv);
                    Delta = std::cbrt(cellVolMsf);
                    DeltaH = Delta;
                } else {
                    Delta = one / dzInv;
                    DeltaH = std::sqrt(one / (dxInv * mf_u(i,j,0) * dyInv * mf_v(i,j,0)));
                }
 
                Real rho = cell_data(i, j, k, Rho_comp);
                Real CsDeltaSqr_h = Cs * Cs * DeltaH * DeltaH;
                Real CsDeltaSqr_v = Cs * Cs * Delta * Delta;
 
                Real nu_turb_base_h = CsDeltaSqr_h * strain_rate_magnitude;
                Real nu_turb_base_v = CsDeltaSqr_v * strain_rate_magnitude;
 
                Real stability_factor = one;
 
                if (l_use_Ri_corr && l_has_xvel && l_has_yvel) {
                    Real N2 = ComputeN2(i, j, k, dzInv, l_abs_g, cell_data, moisture_indices);
                    Real S2_vert = ComputeVerticalShear2(i, j, k, dzInv, u_arr, v_arr);
                    Real Ri = ComputeRichardson(N2, S2_vert);
                    stability_factor = StabilityFunction(Ri, l_Ri_crit);
                }
 
                if (isotropic) {
                    mu_turb(i, j, k, EddyDiff::Mom_h) = rho * nu_turb_base_h * stability_factor;
                    mu_turb(i, j, k, EddyDiff::Mom_v) = rho * nu_turb_base_v * stability_factor;
                } else {
                    mu_turb(i, j, k, EddyDiff::Mom_h) = rho * nu_turb_base_h;
                    mu_turb(i, j, k, EddyDiff::Mom_v) = rho * nu_turb_base_v * stability_factor;
                }
 
                Real dtheta_dz = myhalf * ( cell_data(i,j,k+1,RhoTheta_comp)/cell_data(i,j,k+1,Rho_comp)
                                          - cell_data(i,j,k-1,RhoTheta_comp)/cell_data(i,j,k-1,Rho_comp) )*dzInv;
 
                hfx_x(i,j,k) = zero;
                hfx_y(i,j,k) = zero;
                hfx_z(i,j,k) = -inv_Pr_t * mu_turb(i,j,k,EddyDiff::Mom_v) * dtheta_dz;
            });
        }
    }
    // DEARDORFF: Fill Kturb for momentum in horizontal and vertical
    //***********************************************************************************
    else if (turbChoice.les_type == LESType::Deardorff)
    {
        const Real l_C_k        = turbChoice.Ck;
        const Real l_C_e        = turbChoice.Ce;
        const Real l_C_e_wall   = turbChoice.Ce_wall;
        const Real Ce_lcoeff    = amrex::max(zero, l_C_e - Real(1.9)*l_C_k);
        const Real l_abs_g      = const_grav;
 
        const bool use_ref_theta = (turbChoice.theta_ref > 0);
        const Real l_inv_theta0  = (use_ref_theta) ? one / turbChoice.theta_ref : one;
 
#ifdef _OPENMP
#pragma omp parallel if (Gpu::notInLaunchRegion())
#endif
        for ( MFIter mfi(eddyViscosity,TilingIfNotGPU()); mfi.isValid(); ++mfi)
        {
            Box bxcc  = mfi.tilebox();
 
            const Array4<Real>& mu_turb = eddyViscosity.array(mfi);
            const Array4<Real>& hfx_x   = Hfx1.array(mfi);
            const Array4<Real>& hfx_y   = Hfx2.array(mfi);
            const Array4<Real>& hfx_z   = Hfx3.array(mfi);
            const Array4<Real>& diss    = Diss.array(mfi);
 
            const Array4<Real const > &cell_data = cons_in.array(mfi);
 
            Array4<Real const> mf_u = mapfac[MapFacType::u_x]->const_array(mfi);
            Array4<Real const> mf_v = mapfac[MapFacType::v_y]->const_array(mfi);
 
            Array4<Real const> z_nd_arr = z_phys_nd->const_array(mfi);
 
            ParallelFor(bxcc, [=] AMREX_GPU_DEVICE (int i, int j, int k) noexcept
            {
                Real dxInv = cellSizeInv[0];
                Real dyInv = cellSizeInv[1];
                Real dzInv = cellSizeInv[2];
                if (use_terrain_fitted_coords) {
                    // the terrain grid is only deformed in z for now
                    dzInv /= Compute_h_zeta_AtCellCenter(i,j,k, cellSizeInv, z_nd_arr);
                }
                Real Delta;
                if (isotropic) {
                    Real cellVolMsf = one / (dxInv * mf_u(i,j,0) * dyInv * mf_v(i,j,0) * dzInv);
                    Delta = std::cbrt(cellVolMsf);
                } else {
                    Delta = one / dzInv;
                }
 
                Real dtheta_dz;
                if (use_thetav_grad) {
                    dtheta_dz = myhalf * ( GetThetav(i, j, k+1, cell_data, moisture_indices)
                                          -GetThetav(i, j, k-1, cell_data, moisture_indices) )*dzInv;
                } else if (use_thetal_grad) {
                    dtheta_dz = myhalf * ( GetThetal(i, j, k+1, cell_data, moisture_indices)
                                          -GetThetal(i, j, k-1, cell_data, moisture_indices) )*dzInv;
                } else {
                    dtheta_dz = myhalf * ( cell_data(i, j, k+1, RhoTheta_comp) / cell_data(i, j, k+1, Rho_comp)
                                          -cell_data(i, j, k-1, RhoTheta_comp) / cell_data(i, j, k-1, Rho_comp) )*dzInv;
                }
 
                // Calculate stratification-dependent mixing length (Deardorff 1980, Eqn. 10a)
                Real E              = amrex::max(cell_data(i,j,k,RhoKE_comp)/cell_data(i,j,k,Rho_comp),Real(0.0));
                Real stratification = l_abs_g * dtheta_dz * l_inv_theta0;
                if (!use_ref_theta) {
                    // l_inv_theta0 == 1, divide by actual theta
                    stratification *= cell_data(i,j,k,Rho_comp) /
                                      cell_data(i,j,k,RhoTheta_comp);
                }
 
                // Following WRF, the stratification effects are applied to the vertical length scales
                // in the case of anisotropic mixing
                Real length;
                Real eps       = std::numeric_limits<Real>::epsilon();
                if (stratification <= eps) {
                    length = Delta;  // cbrt(dx*dy*dz) -or- dz
                } else {
                    length = Real(0.76) * std::sqrt(E / amrex::max(stratification,eps));
                    // mixing length should be _reduced_ for stable stratification
                    length = amrex::min(length, Delta);
                    // following WRF, make sure the mixing length isn't too small
                    length = amrex::max(length, Real(0.001) * Delta);
                }
 
                Real DeltaH = (isotropic) ? length : std::sqrt(one / (dxInv * mf_u(i,j,0) * dyInv * mf_v(i,j,0)));
 
                Real Pr_inv_v = (one + two*length/Delta);
                Real Pr_inv_h  = (isotropic) ? Pr_inv_v : inv_Pr_t;
 
                // Calculate eddy diffusivities
                // K = rho * C_k * l * KE^(1/2)
                mu_turb(i,j,k,EddyDiff::Mom_h) = cell_data(i,j,k,Rho_comp) * l_C_k * DeltaH * std::sqrt(E);
                mu_turb(i,j,k,EddyDiff::Mom_v) = cell_data(i,j,k,Rho_comp) * l_C_k * length * std::sqrt(E);
                // KH = (1 + 2*l/delta) * mu_turb
                mu_turb(i,j,k,EddyDiff::Theta_h) = Pr_inv_h * mu_turb(i,j,k,EddyDiff::Mom_h);
                mu_turb(i,j,k,EddyDiff::Theta_v) = Pr_inv_v * mu_turb(i,j,k,EddyDiff::Mom_v);
                // Store lengthscale for TKE source terms
                mu_turb(i,j,k,EddyDiff::Turb_lengthscale) = length;
 
                // Calculate SFS quantities
                // - dissipation
                Real Ce;
                if ((l_C_e_wall > 0) && (k==0)) {
                    Ce = l_C_e_wall;
                } else {
                    Ce = Real(1.9)*l_C_k + Ce_lcoeff*length / Delta;
                }
                diss(i,j,k) = cell_data(i,j,k,Rho_comp) * Ce * std::pow(E,Real(1.5)) / length;
 
                // - heat flux
                //   (Note: If using SurfaceLayer, the value at k=0 will
                //    be overwritten)
                hfx_x(i,j,k) = zero;
                hfx_y(i,j,k) = zero;
                hfx_z(i,j,k) = -mu_turb(i,j,k,EddyDiff::Theta_v) * dtheta_dz; // (rho*w)' theta' [kg m^-2 s^-1 K]
            });
        }
    }
 
    // Extrapolate Kturb in x/y, fill remaining elements (relevant to lev==0)
    //***********************************************************************************
    int ngc(1);
    // EddyDiff mapping :   Theta_h     KE_h       Scalar_h    Q_h
    Vector<Real> Factors = {inv_Pr_t, inv_sigma_k, inv_Sc_t, inv_Sc_t}; // alpha = mu/Pr
    Gpu::AsyncVector<Real> d_Factors; d_Factors.resize(Factors.size());
    Gpu::copy(Gpu::hostToDevice, Factors.begin(), Factors.end(), d_Factors.begin());
    Real* fac_ptr = d_Factors.data();
 
    const bool use_KE = ( turbChoice.les_type == LESType::Deardorff );
 
#ifdef _OPENMP
#pragma omp parallel if (Gpu::notInLaunchRegion())
#endif
    for ( MFIter mfi(eddyViscosity,TilingIfNotGPU()); mfi.isValid(); ++mfi)
    {
        Box bxcc   = mfi.tilebox();
        Box planex = bxcc; planex.setSmall(0, 1); planex.setBig(0, ngc); planex.grow(1,1);
        Box planey = bxcc; planey.setSmall(1, 1); planey.setBig(1, ngc); planey.grow(0,1);
        bxcc.growLo(0,ngc); bxcc.growHi(0,ngc);
        bxcc.growLo(1,ngc); bxcc.growHi(1,ngc);
 
        const Array4<Real>& mu_turb = eddyViscosity.array(mfi);
 
        for (auto n = 1; n < EddyDiff::Mom_v; ++n) {
            int offset = EddyDiff::Mom_v;
            switch (n)
            {
             case EddyDiff::KE_h:
                if (use_KE) {
                   ParallelFor(bxcc, [=] AMREX_GPU_DEVICE (int i, int j, int k) noexcept
                   {
                       int indx   = n;
                       int indx_v = indx + offset;
                       mu_turb(i,j,k,indx)   = mu_turb(i,j,k,EddyDiff::Mom_h) * fac_ptr[indx-1];
                       mu_turb(i,j,k,indx_v) = mu_turb(i,j,k,EddyDiff::Mom_v) * fac_ptr[indx-1];
                   });
                }
                break;
            default:
                ParallelFor(bxcc, [=] AMREX_GPU_DEVICE (int i, int j, int k) noexcept
                {
                    int indx   = n;
                    int indx_v = indx + offset;
 
                    // NOTE: Theta_h, Theta_v have already been set for Deardorff
                    if (!(indx_v == EddyDiff::Theta_v && use_KE)) {
                        mu_turb(i,j,k,indx)   = mu_turb(i,j,k,EddyDiff::Mom_h) * fac_ptr[indx-1];
                        mu_turb(i,j,k,indx_v) = mu_turb(i,j,k,EddyDiff::Mom_v) * fac_ptr[indx-1];
                    }
                });
                break;
          }
       }
    }
}

Referenced by ComputeTurbulentViscosity().

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ComputeTurbulentViscosityLES_EB()

void ComputeTurbulentViscosityLES_EB	(	Vector< std::unique_ptr< MultiFab >> &	Tau_lev,
		const MultiFab &	cons_in,
		MultiFab &	eddyViscosity,
		MultiFab &	Hfx1,
		MultiFab &	Hfx2,
		MultiFab &	Hfx3,
		const Geometry &	geom,
		Vector< std::unique_ptr< MultiFab >> &	mapfac,
		const TurbChoice &	turbChoice,
		const Real	const_grav,
		[[maybe_unused] ] const SolverChoice &	solverChoice,
		std::unique_ptr< SurfaceLayer > &	,
		const MoistureComponentIndices &	moisture_indices,
		const eb_ &	ebfact,
		const MultiFab *	xvel,
		const MultiFab *	yvel
	)

{
    const GpuArray<Real, AMREX_SPACEDIM> cellSizeInv = geom.InvCellSizeArray();
    Real dxInv = cellSizeInv[0];
    Real dyInv = cellSizeInv[1];
    Real dzInv = cellSizeInv[2];
 
    const Box& domain = geom.Domain();
 
    Real inv_Pr_t    = turbChoice.Pr_t_inv;
    Real inv_Sc_t    = turbChoice.Sc_t_inv;
    Real inv_sigma_k = one / turbChoice.sigma_k;
 
    bool isotropic = turbChoice.mix_isotropic;
 
    AMREX_ASSERT(turbChoice.les_type == LESType::Smagorinsky);
 
    // SMAGORINSKY: Fill Kturb for momentum in horizontal and vertical
    //***********************************************************************************
    if (turbChoice.les_type == LESType::Smagorinsky)
    {
        Real Cs = turbChoice.Cs;
 
        // Define variables required inside device lambdas (scalars only)
        Real l_abs_g = const_grav;
        Real l_Ri_crit = turbChoice.Ri_crit;
        bool l_use_Ri_corr = turbChoice.use_Ri_correction;
        bool l_has_xvel = (xvel != nullptr);
        bool l_has_yvel = (yvel != nullptr);
 
#ifdef _OPENMP
#pragma omp parallel if (Gpu::notInLaunchRegion())
#endif
        for (MFIter mfi(eddyViscosity,TilingIfNotGPU()); mfi.isValid(); ++mfi)
        {
            Box bxcc  = mfi.growntilebox(1) & domain;
            const Array4<Real>& mu_turb = eddyViscosity.array(mfi);
            const Array4<Real>& hfx_x   = Hfx1.array(mfi);
            const Array4<Real>& hfx_y   = Hfx2.array(mfi);
            const Array4<Real>& hfx_z   = Hfx3.array(mfi);
            const Array4<Real const >& cell_data = cons_in.array(mfi);
            Array4<Real const> tau11 = Tau_lev[TauType::tau11]->array(mfi);
            Array4<Real const> tau22 = Tau_lev[TauType::tau22]->array(mfi);
            Array4<Real const> tau33 = Tau_lev[TauType::tau33]->array(mfi);
            Array4<Real const> tau12 = Tau_lev[TauType::tau12]->array(mfi);
            Array4<Real const> tau13 = Tau_lev[TauType::tau13]->array(mfi);
            Array4<Real const> tau23 = Tau_lev[TauType::tau23]->array(mfi);
            Array4<Real const> mf_u = mapfac[MapFacType::u_x]->const_array(mfi);
            Array4<Real const> mf_v = mapfac[MapFacType::v_y]->const_array(mfi);
 
            Array4<Real const> u_arr = (l_has_xvel) ? xvel->const_array(mfi) : Array4<Real const>{};
            Array4<Real const> v_arr = (l_has_yvel) ? yvel->const_array(mfi) : Array4<Real const>{};
 
            Array4<const EBCellFlag> c_cflag = (ebfact.get_const_factory())->getMultiEBCellFlagFab()[mfi].const_array();
            Array4<const EBCellFlag> u_cflag = (ebfact.get_u_const_factory())->getMultiEBCellFlagFab()[mfi].const_array();
            Array4<const EBCellFlag> v_cflag = (ebfact.get_v_const_factory())->getMultiEBCellFlagFab()[mfi].const_array();
            Array4<const EBCellFlag> w_cflag = (ebfact.get_w_const_factory())->getMultiEBCellFlagFab()[mfi].const_array();
            Array4<const Real      > u_vfrac = (ebfact.get_u_const_factory())->getVolFrac().const_array(mfi);
            Array4<const Real      > v_vfrac = (ebfact.get_v_const_factory())->getVolFrac().const_array(mfi);
 
            ParallelFor(bxcc, [=] AMREX_GPU_DEVICE (int i, int j, int k) noexcept
            {
                if (!c_cflag(i,j,k).isCovered()) {
                    // =====================================================================
                    // 1. STRAIN RATE MAGNITUDE CALCULATION
                    // =====================================================================
                    Real SmnSmn = zero;
                    if (c_cflag(i,j,k).isRegular()) {
                        SmnSmn = ComputeSmnSmn(i,j,k,tau11,tau22,tau33,tau12,tau13,tau23);
                    } else if (c_cflag(i,j,k).isSingleValued()) {
                        SmnSmn = ComputeSmnSmn_EB(i,j,k,tau11,tau22,tau33,tau12,tau13,tau23,c_cflag,u_cflag,v_cflag,w_cflag);
                    }
                    Real strain_rate_magnitude = std::sqrt(two * SmnSmn);
 
                    // =====================================================================
                    // 2. GRID SCALE CALCULATION (filter width Δ)
                    // =====================================================================
                    Real Delta;
                    Real DeltaH;
                    if (isotropic) {
                        Real cellVolMsf = one / (dxInv * mf_u(i,j,0) * dyInv * mf_v(i,j,0) * dzInv);
                        Delta = std::cbrt(cellVolMsf);
                        DeltaH = Delta;
                    } else {
                        Delta = one / dzInv;
                        DeltaH = std::sqrt(one / (dxInv * mf_u(i,j,0) * dyInv * mf_v(i,j,0)));
                    }
 
                    Real rho = cell_data(i, j, k, Rho_comp);
                    Real CsDeltaSqr_h = Cs * Cs * DeltaH * DeltaH;
                    Real CsDeltaSqr_v = Cs * Cs * Delta * Delta;
 
                    Real nu_turb_base_h = CsDeltaSqr_h * strain_rate_magnitude;
                    Real nu_turb_base_v = CsDeltaSqr_v * strain_rate_magnitude;
 
                    Real stability_factor = one;
 
                    if (l_use_Ri_corr && l_has_xvel && l_has_yvel) {
                        Real N2 = zero;
                        Real S2_vert = zero;
                        if (c_cflag(i,j,k).isRegular()) {
                            N2 = ComputeN2(i, j, k, dzInv, l_abs_g, cell_data, moisture_indices);
                            S2_vert = ComputeVerticalShear2(i, j, k, dzInv, u_arr, v_arr);
                        } else if (c_cflag(i,j,k).isSingleValued()) {
                            N2 = ComputeN2_EB(i, j, k, c_cflag, dzInv, l_abs_g, cell_data, moisture_indices);
                            S2_vert = ComputeVerticalShear2_EB(i, j, k, c_cflag, u_vfrac, v_vfrac, dzInv, u_arr, v_arr);
                        }
                        Real Ri = ComputeRichardson(N2, S2_vert);
                        stability_factor = StabilityFunction(Ri, l_Ri_crit);
                    }
 
                    if (isotropic) {
                        mu_turb(i, j, k, EddyDiff::Mom_h) = rho * nu_turb_base_h * stability_factor;
                        mu_turb(i, j, k, EddyDiff::Mom_v) = rho * nu_turb_base_v * stability_factor;
                    } else {
                        mu_turb(i, j, k, EddyDiff::Mom_h) = rho * nu_turb_base_h;
                        mu_turb(i, j, k, EddyDiff::Mom_v) = rho * nu_turb_base_v * stability_factor;
                    }
 
                    Real dtheta_dz = zero;
 
                    if (c_cflag(i,j,k).isSingleValued() && c_cflag(i,j,k+1).isCovered()) {
                        amrex::Real theta    = cell_data(i, j, k,   RhoTheta_comp) / rho;
                        amrex::Real theta_km1 = cell_data(i,j,k-1,RhoTheta_comp)/cell_data(i,j,k-1,Rho_comp);
                        amrex::Real theta_km2 = cell_data(i,j,k-2,RhoTheta_comp)/cell_data(i,j,k-2,Rho_comp);
                        dtheta_dz = (three*theta - Real(4.)*theta_km1 + theta_km2) * myhalf * dzInv;
                    } else if (c_cflag(i,j,k).isSingleValued() && c_cflag(i,j,k-1).isCovered()) {
                        amrex::Real theta    = cell_data(i, j, k,   RhoTheta_comp) / rho;
                        amrex::Real theta_kp1 = cell_data(i,j,k+1,RhoTheta_comp)/cell_data(i,j,k+1,Rho_comp);
                        amrex::Real theta_kp2 = cell_data(i,j,k+2,RhoTheta_comp)/cell_data(i,j,k+2,Rho_comp);
                        dtheta_dz = (-theta_kp2 + Real(4.)*theta_kp1 - three*theta) * myhalf * dzInv;
                    } else if (!c_cflag(i,j,k).isCovered()) {
                        amrex::Real theta_km1 = cell_data(i,j,k-1,RhoTheta_comp)/cell_data(i,j,k-1,Rho_comp);
                        amrex::Real theta_kp1 = cell_data(i,j,k+1,RhoTheta_comp)/cell_data(i,j,k+1,Rho_comp);
                        dtheta_dz = myhalf * (theta_kp1 - theta_km1) * dzInv;
                    }
 
                    hfx_x(i,j,k) = zero;
                    hfx_y(i,j,k) = zero;
                    hfx_z(i,j,k) = -inv_Pr_t * mu_turb(i,j,k,EddyDiff::Mom_v) * dtheta_dz;
 
                } else {
 
                    hfx_x(i,j,k) = zero;
                    hfx_y(i,j,k) = zero;
                    hfx_z(i,j,k) = zero;
                }// End of if not covered
            });
        }
    }
 
    // Extrapolate Kturb in x/y, fill remaining elements (relevant to lev==0)
    //***********************************************************************************
    int ngc(1);
    // EddyDiff mapping :   Theta_h     KE_h       Scalar_h    Q_h
    Vector<Real> Factors = {inv_Pr_t, inv_sigma_k, inv_Sc_t, inv_Sc_t}; // alpha = mu/Pr
    Gpu::AsyncVector<Real> d_Factors; d_Factors.resize(Factors.size());
    Gpu::copy(Gpu::hostToDevice, Factors.begin(), Factors.end(), d_Factors.begin());
    Real* fac_ptr = d_Factors.data();
 
    const bool use_KE = ( turbChoice.les_type == LESType::Deardorff );
 
#ifdef _OPENMP
#pragma omp parallel if (Gpu::notInLaunchRegion())
#endif
    for ( MFIter mfi(eddyViscosity,TilingIfNotGPU()); mfi.isValid(); ++mfi)
    {
        Box bxcc   = mfi.tilebox();
        Box planex = bxcc; planex.setSmall(0, 1); planex.setBig(0, ngc); planex.grow(1,1);
        Box planey = bxcc; planey.setSmall(1, 1); planey.setBig(1, ngc); planey.grow(0,1);
        bxcc.growLo(0,ngc); bxcc.growHi(0,ngc);
        bxcc.growLo(1,ngc); bxcc.growHi(1,ngc);
 
        const Array4<Real>& mu_turb = eddyViscosity.array(mfi);
 
        for (auto n = 1; n < EddyDiff::Mom_v; ++n) {
            int offset = EddyDiff::Mom_v;
            switch (n)
            {
             case EddyDiff::KE_h:
                if (use_KE) {
                   ParallelFor(bxcc, [=] AMREX_GPU_DEVICE (int i, int j, int k) noexcept
                   {
                       int indx   = n;
                       int indx_v = indx + offset;
                       mu_turb(i,j,k,indx)   = mu_turb(i,j,k,EddyDiff::Mom_h) * fac_ptr[indx-1];
                       mu_turb(i,j,k,indx_v) = mu_turb(i,j,k,EddyDiff::Mom_v) * fac_ptr[indx-1];
                   });
                }
                break;
            default:
                ParallelFor(bxcc, [=] AMREX_GPU_DEVICE (int i, int j, int k) noexcept
                {
                    int indx   = n;
                    int indx_v = indx + offset;
 
                    // NOTE: Theta_h, Theta_v have already been set for Deardorff
                    if (!(indx_v == EddyDiff::Theta_v && use_KE)) {
                        mu_turb(i,j,k,indx)   = mu_turb(i,j,k,EddyDiff::Mom_h) * fac_ptr[indx-1];
                        mu_turb(i,j,k,indx_v) = mu_turb(i,j,k,EddyDiff::Mom_v) * fac_ptr[indx-1];
                    }
                });
                break;
          }
       }
    }
}

Referenced by ComputeTurbulentViscosity().

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ComputeTurbulentViscosityRANS()

void ComputeTurbulentViscosityRANS	(	Vector< std::unique_ptr< MultiFab >> &	,
		const MultiFab &	cons_in,
		const MultiFab &	wdist,
		MultiFab &	eddyViscosity,
		MultiFab &	Hfx1,
		MultiFab &	Hfx2,
		MultiFab &	Hfx3,
		MultiFab &	Diss,
		const Geometry &	geom,
		bool	use_terrain_fitted_coords,
		Vector< std::unique_ptr< MultiFab >> &	,
		const std::unique_ptr< MultiFab > &	z_phys_nd,
		const TurbChoice &	turbChoice,
		const Real	const_grav,
		std::unique_ptr< SurfaceLayer > &	SurfLayer,
		const MultiFab *	z_0
	)

Function for computing the eddy viscosity with RANS.

Parameters

[in]	cons_in	cell center conserved quantities
[in]	wdist	wall distance
[out]	eddyViscosity	turbulent viscosity
[out]	Hfx1	heat flux in x-dir
[out]	Hfx2	heat flux in y-dir
[out]	Hfx3	heat flux in z-dir
[out]	Diss	dissipation of turbulent kinetic energy
[in]	geom	problem geometry
[in]	use_terrain_fitted_coords	flag for terrain-fitted coordinates
[in]	z_phys_nd	nodal physical z coordinates
[in]	turbChoice	container with turbulence parameters
[in]	const_grav	gravitational acceleration
[in]	SurfLayer	optional surface-layer model
[in]	z_0	roughness length

{
    const GpuArray<Real, AMREX_SPACEDIM> cellSizeInv = geom.InvCellSizeArray();
    const bool use_SurfLayer = (SurfLayer != nullptr);
 
    Real inv_Pr_t    = turbChoice.Pr_t_inv;
    Real inv_Sc_t    = turbChoice.Sc_t_inv;
    Real inv_sigma_k = one / turbChoice.sigma_k;
 
    // One-Equation k model (Axell & Liungman 2001, Environ Fluid Mech)
    //***********************************************************************************
    if (turbChoice.rans_type == RANSType::kEqn)
    {
        const Real Cmu0       = turbChoice.Cmu0;
        const Real Cmu0_pow3  = Cmu0 * Cmu0 * Cmu0;
        const Real inv_Cb_sq  = one / (turbChoice.Cb * turbChoice.Cb);
        const Real Rt_crit    = turbChoice.Rt_crit;
        const Real Rt_min     = turbChoice.Rt_min;
        const Real l_g_max    = turbChoice.l_g_max;
        const Real abs_g      = const_grav;
 
        const bool use_ref_theta = (turbChoice.theta_ref > 0);
        const Real inv_theta0  = (use_ref_theta) ? one / turbChoice.theta_ref : one;
 
#ifdef _OPENMP
#pragma omp parallel if (Gpu::notInLaunchRegion())
#endif
        for ( MFIter mfi(eddyViscosity,TilingIfNotGPU()); mfi.isValid(); ++mfi)
        {
            Box bxcc = mfi.tilebox();
 
            const Array4<Real const>& d_arr  = wdist.const_array(mfi);
            const Array4<Real const>& z0_arr = (use_SurfLayer) ? z_0->const_array(mfi) : Array4<Real const>{};
 
            const Array4<Real>& mu_turb = eddyViscosity.array(mfi);
            const Array4<Real>& hfx_x   = Hfx1.array(mfi);
            const Array4<Real>& hfx_y   = Hfx2.array(mfi);
            const Array4<Real>& hfx_z   = Hfx3.array(mfi);
            const Array4<Real>& diss    = Diss.array(mfi);
 
            const Array4<Real const>& cell_data = cons_in.array(mfi);
 
            const Array4<Real const>& z_nd_arr = z_phys_nd->const_array(mfi);
 
            ParallelFor(bxcc, [=] AMREX_GPU_DEVICE (int i, int j, int k) noexcept
            {
                Real eps = std::numeric_limits<Real>::epsilon();
                Real tke = amrex::max(cell_data(i,j,k,RhoKE_comp)/cell_data(i,j,k,Rho_comp), eps);
 
                // Estimate stratification
                Real dzInv = cellSizeInv[2];
                if (use_terrain_fitted_coords) {
                    // the terrain grid is only deformed in z for now
                    dzInv /= Compute_h_zeta_AtCellCenter(i,j,k, cellSizeInv, z_nd_arr);
                }
                Real dtheta_dz = myhalf * ( cell_data(i,j,k+1,RhoTheta_comp)/cell_data(i,j,k+1,Rho_comp)
                                          - cell_data(i,j,k-1,RhoTheta_comp)/cell_data(i,j,k-1,Rho_comp) )*dzInv;
                Real N2 = abs_g * inv_theta0 * dtheta_dz; // Brunt–Väisälä frequency squared
                if (!use_ref_theta) {
                    // inv_theta0 == 1, divide by actual theta
                    N2 *= cell_data(i,j,k,Rho_comp) /
                          cell_data(i,j,k,RhoTheta_comp);
                }
 
                // Geometric length scale (AL01, Eqn. 22)
                Real l_g = (z0_arr) ? KAPPA * (d_arr(i, j, k) + z0_arr(i, j, 0))
                                    : KAPPA * d_arr(i, j, k);
 
                // Enforce a maximum value
                l_g = l_g_max * l_g / (l_g_max + l_g);
 
                // Turbulent length scale
                Real length, Rt;
                if (std::abs(N2) <= eps) {
                    length = l_g;
                } else if (N2 > eps) {
                    // Stable (AL01, Eqn. 26)
                    length = std::sqrt(one /
                            (one / (l_g * l_g) + inv_Cb_sq * N2 / tke));
                } else {
                    Real diss0 = Cmu0_pow3 * std::pow(tke,Real(1.5)) / l_g; // approx
                    Rt = tke*tke * N2 / (diss0*diss0);
 
                    // Unstable (AL01, Eqn. 28)
                    // - predict
                    length = l_g * std::sqrt(one - Cmu0_pow3*Cmu0_pow3 * inv_Cb_sq * Rt);
                    // - correct
                    diss0 = Cmu0_pow3 * std::pow(tke,Real(1.5)) / length;
                    Rt = tke*tke * N2 / (diss0*diss0);
                    length  = l_g * std::sqrt(one - Cmu0_pow3*Cmu0_pow3 * inv_Cb_sq * Rt);
                }
                mu_turb(i, j, k, EddyDiff::Turb_lengthscale) = length;
 
                // Dissipation rate (AL01, Eqn. 19)
                diss(i, j, k) = cell_data(i, j, k, Rho_comp) * Cmu0_pow3 * std::pow(tke,Real(1.5)) / length;
 
                // Turbulent Richardson number (AL01, Eqn. 29)
                //Real Rt = tke*tke * N2 / (diss(i,j,k)*diss(i,j,k));
                Rt = length*length * N2 / (tke * Cmu0_pow3 * Cmu0_pow3); // combined with Eqn. 19
 
                // Burchard & Petersen smoothing function
                Rt = (Rt >= Rt_crit) ? Rt : std::max(Rt, Rt - (Rt - Rt_crit)*(Rt - Rt_crit) / (Rt + Rt_min - 2*Rt_crit));
 
                // Stability functions
                // Note: These use the smoothed turbulent Richardson number
                Real cmu = (Cmu0 + Real(0.108)*Rt)
                         / (one + Real(0.308)*Rt + Real(0.00837)*Rt*Rt); // (AL01, Eqn. 31)
                Real cmu_prime = Cmu0 / (1 + Real(0.277)*Rt); // (AL01, Eqn. 32)
 
                // Calculate eddy diffusivities
                // K = rho * nu_t = rho * c_mu * tke^(1/2) * length
                Real nut = cmu * std::sqrt(tke) * length; // eddy viscosity
                Real nut_prime = cmu_prime / cmu * nut;   // eddy diffusivity
                mu_turb(i, j, k, EddyDiff::Mom_h) = cell_data(i, j, k, Rho_comp) * nut;
                mu_turb(i, j, k, EddyDiff::Mom_v) = mu_turb(i, j, k, EddyDiff::Mom_h);
                mu_turb(i, j, k, EddyDiff::Theta_v) = cell_data(i, j, k, Rho_comp) * nut_prime;
 
                // Calculate heat flux
                // - If using SurfaceLayer, the value at k=0 will be overwritten
                hfx_x(i, j, k) = zero;
                hfx_y(i, j, k) = zero;
                // Note: buoyant production = g/theta0 * hfx == -nut_prime * N^2 (c.f. AL01 Eqn. 15)
                //                          = nut_prime * g/theta0 * dtheta/dz
                //                  ==> hfx = nut_prime * dtheta/dz
                //   Our convention is such that dtheta/dz < 0 gives a positive
                //   (upward) heat flux.
                hfx_z(i, j, k) = -mu_turb(i, j, k, EddyDiff::Theta_v) * dtheta_dz; // (rho*w)' theta' [kg m^-2 s^-1 K]
            });
        }
    }
 
    // Extrapolate Kturb in x/y, fill remaining elements (relevant to lev==0)
    //***********************************************************************************
    int ngc(1);
    // EddyDiff mapping :   Theta_h     KE_h       Scalar_h    Q_h
    Vector<Real> Factors = {inv_Pr_t, inv_sigma_k, inv_Sc_t, inv_Sc_t}; // alpha = mu/Pr
    Gpu::AsyncVector<Real> d_Factors; d_Factors.resize(Factors.size());
    Gpu::copy(Gpu::hostToDevice, Factors.begin(), Factors.end(), d_Factors.begin());
    Real* fac_ptr = d_Factors.data();
 
    const bool use_KE = ( turbChoice.rans_type == RANSType::kEqn );
 
#ifdef _OPENMP
#pragma omp parallel if (Gpu::notInLaunchRegion())
#endif
    for ( MFIter mfi(eddyViscosity,TilingIfNotGPU()); mfi.isValid(); ++mfi)
    {
        Box bxcc   = mfi.tilebox();
        Box planex = bxcc; planex.setSmall(0, 1); planex.setBig(0, ngc); planex.grow(1,1);
        Box planey = bxcc; planey.setSmall(1, 1); planey.setBig(1, ngc); planey.grow(0,1);
        bxcc.growLo(0,ngc); bxcc.growHi(0,ngc);
        bxcc.growLo(1,ngc); bxcc.growHi(1,ngc);
 
        const Array4<Real>& mu_turb = eddyViscosity.array(mfi);
 
        for (auto n = 1; n < EddyDiff::Mom_v; ++n) {
            int offset = EddyDiff::Mom_v;
            switch (n)
            {
             case EddyDiff::KE_h:
                if (use_KE) {
                   ParallelFor(bxcc, [=] AMREX_GPU_DEVICE (int i, int j, int k) noexcept
                   {
                       int indx   = n;
                       int indx_v = indx + offset;
                       mu_turb(i,j,k,indx)   = mu_turb(i,j,k,EddyDiff::Mom_h) * fac_ptr[indx-1];
                       mu_turb(i,j,k,indx_v) = mu_turb(i,j,k,indx);
                   });
                }
                break;
            default:
                ParallelFor(bxcc, [=] AMREX_GPU_DEVICE (int i, int j, int k) noexcept
                {
                    int indx   = n;
                    int indx_v = indx + offset;
 
                    mu_turb(i,j,k,indx)   = mu_turb(i,j,k,EddyDiff::Mom_h) * fac_ptr[indx-1];
 
                    // NOTE: Theta_v has already been set for Deardorff
                    if (!(indx_v == EddyDiff::Theta_v && use_KE)) {
                        mu_turb(i,j,k,indx_v) = mu_turb(i,j,k,indx);
                    }
                });
                break;
          }
       }
    }
}

Referenced by ComputeTurbulentViscosity().

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