ERF_TerrainImplicitMetric.H File Reference

#include <AMReX_REAL.H>
#include <AMReX_GpuQualifiers.H>

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Functions
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real	TerrainMetricMomFactor (const int stagdir, const amrex::Real h_xi, const amrex::Real h_eta, const amrex::Real mx, const amrex::Real my) noexcept
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real	TerrainMetricScalarFactor (const amrex::Real h_xi, const amrex::Real h_eta, const amrex::Real mx, const amrex::Real my) noexcept
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE bool	TerrainMetricImplicitFace (const int kface, const int dom_lo, const int dom_hi) noexcept

Function Documentation

TerrainMetricImplicitFace()

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE bool TerrainMetricImplicitFace ( const int  kface, const int  dom_lo, const int  dom_hi  )

noexcept

The split applies on the faces the implicit solve treats with a coefficient: every zeta face strictly inside the domain (dom_lo < kface <= dom_hi, with dom_hi the top cell). The bottom and top faces carry the boundary condition (wall, surface layer, Neumann) and stay explicit.

{
    return (kface > dom_lo) && (kface <= dom_hi);
}

Referenced by SubtractTerrainMetricImplicitPart_T_Impl().

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TerrainMetricMomFactor()

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real TerrainMetricMomFactor ( const int  stagdir, const amrex::Real  h_xi, const amrex::Real  h_eta, const amrex::Real  mx, const amrex::Real  my  )

noexcept

Terrain-metric part of the vertical diffusion on a terrain-fitted mesh, for erf.implicit_terrain_metric.

The flux through a zeta face projects the horizontal fluxes onto the face normal. Their h*d/dz parts add a vertical-diffusion term K_h * M * d/dz to the zeta flux, with the factors below. The explicit operator forms it from averaged horizontal fluxes; with the option on, the same term in compact form (face differences in zeta) is also put into the implicit vertical solve and subtracted explicitly at the state the explicit terms see, so the stages with an implicit solve treat the K_h * M * d2/dz2 stiffness implicitly. The factors are the exact du/dz (dphi/dz) content of the projected fluxes, so for smooth fields on a uniform slope the explicit remainder (averaged minus compact) is small; at the grid scale it is the whole compact term with the opposite sign, cancelled within the stage by the implicit solve, which is why every stage needs the solve (SolverChoice::check_params).

h_xi and h_eta are the terrain slopes dz/dxi and dz/deta at the face, mx and my the map factors there. Momentum: the zeta flux of u holds -0.5 * mu_h_tot * M_u * du/dz with M_u = (4/3) (h_xi mx)^2 + (h_eta my)^2, from h_xi (S11 - er/3) and h_eta S12: S11 carries -h_xi mx du/dz, and the expansion rate er carries the same term through Omega, so the deviatoric S11 - er/3 carries -(2/3) h_xi mx du/dz. For v, M_v = (h_xi mx)^2 + (4/3) (h_eta my)^2, from h_xi S12 and h_eta (S22 - er/3).

Parameters

[in]

stagdir

0 for u, 1 for v

{
    const amrex::Real ax = h_xi * mx;
    const amrex::Real ay = h_eta * my;
    const amrex::Real four_thirds = amrex::Real(4.0) / amrex::Real(3.0);
    return (stagdir == 0) ? four_thirds*ax*ax + ay*ay
                          : ax*ax + four_thirds*ay*ay;
}

Referenced by ComputeStressConsVisc_T(), and ComputeStressVarVisc_T().

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TerrainMetricScalarFactor()

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::Real TerrainMetricScalarFactor ( const amrex::Real  h_xi, const amrex::Real  h_eta, const amrex::Real  mx, const amrex::Real  my  )

noexcept

Scalars: G_z = F_z - h_xi mx Fx_bar - h_eta my Fy_bar holds -K_h * M_s * dphi/dz with M_s = (h_xi mx)^2 + (h_eta my)^2.

{
    const amrex::Real ax = h_xi * mx;
    const amrex::Real ay = h_eta * my;
    return ax*ax + ay*ay;
}

Referenced by SubtractTerrainMetricImplicitPart_T_Impl().

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