ERF_InitCustomPertVels_CouettePoiseuille.H

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    Real U_0   = zero;
    Real V_0   = zero;
    Real W_0   = zero;
 
    ParmParse pp_for_pert_vels("prob");
 
    pp_for_pert_vels.query("U_0", U_0);
    pp_for_pert_vels.query("V_0", V_0);
    pp_for_pert_vels.query("W_0", W_0);
 
    int prob_type;
    pp_for_pert_vels.get("prob_type", prob_type);
 
    AMREX_ALWAYS_ASSERT (prob_type == 1 ||
                         prob_type == 10 || prob_type == 11 ||
                         prob_type == 20 || prob_type == 21);
 
 
    Real pert_periods_u = amrex::Real(5.0); pp_for_pert_vels.query("pert_periods_u", pert_periods_u);
    Real pert_periods_v = amrex::Real(5.0); pp_for_pert_vels.query("pert_periods_v", pert_periods_v);
 
    Real pert_delta_u = zero; pp_for_pert_vels.query("pert_delta_u", pert_delta_u);
    Real pert_delta_v = zero; pp_for_pert_vels.query("pert_delta_u", pert_delta_v);
 
    Real pert_lo = -1e34; pp_for_pert_vels.query("pert_lo", pert_lo);
    Real pert_hi =  1e34; pp_for_pert_vels.query("pert_hi", pert_hi);
 
    auto problo = geomdata.ProbLo();
    auto probhi = geomdata.ProbHi();
 
    Real aval = pert_periods_u * two * PI / (probhi[1] - problo[1]);
    Real bval = pert_periods_v * two * PI / (probhi[0] - problo[0]);
 
    // Couette flow
    if (prob_type == 1) {
 
        ParallelFor(xbx, [=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept {
            const auto *const prob_hi  = geomdata.ProbHi();
            const auto *const dx       = geomdata.CellSize();
            const Real z = (k + myhalf) * dx[2];
            x_vel_pert(i, j, k) = U_0 * z / prob_hi[2];
        });
 
        ParallelFor(ybx, [=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept {
            const auto *const prob_hi  = geomdata.ProbHi();
            const auto *const dx       = geomdata.CellSize();
            const Real z = (k + myhalf) * dx[2];
            y_vel_pert(i, j, k) = V_0 * z / prob_hi[2];
        });
 
        ParallelFor(zbx, [=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept {
            z_vel_pert(i, j, k) = W_0;
        });
 
    // Poiseuille flow
    } else if (prob_type == 10 || prob_type == 11) {
 
        ParallelFor(xbx, [=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept
        {
            const Real* prob_lo = geomdata.ProbLo();
            const Real* dx      = geomdata.CellSize();
            const Real z_h = prob_lo[2] + (k + myhalf) *  dx[2];
 
            // Set the x-velocity to be a parabolic profile with max 1 at z = 0 and 0 at z = +/-1
            if (prob_type == 10) {
                x_vel_pert(i, j, k) = one - z_h * z_h;
            } else {
                x_vel_pert(i, j, k) = zero;
            }
        });
 
        ParallelFor(ybx, [=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept
        {
            const Real* prob_lo = geomdata.ProbLo();
            const Real* dx      = geomdata.CellSize();
            const Real z_h = prob_lo[2] + (k + myhalf) *  dx[2];
 
            // Set the x-velocity to be a parabolic profile with max 1 at z = 0 and 0 at z = +/-1
            if (prob_type == 11) {
               y_vel_pert(i, j, k) = one - z_h * z_h;
            } else {
               y_vel_pert(i, j, k) = zero;
            }
        });
 
        ParallelFor(zbx, [=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept
        {
            z_vel_pert(i, j, k) = zero;
        });
 
    // plane channel flow initialization
    } else if (prob_type == 20 || prob_type == 21) {
 
        ParallelFor(xbx, [=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept
        {
            const Real* prob_lo = geomdata.ProbLo();
            const Real* prob_hi = geomdata.ProbHi();
            const Real* dx      = geomdata.CellSize();
 
 
            const Real z = fourth*( z_nd(i,j  ,k) + z_nd(i,j  ,k+1) + z_nd(i,j+1,k) + z_nd(i,j+1,k+1) );
 
            // Normalized wall-normal dist between -1 and 1
            Real y_h = (prob_type == 20) ? two * (j + myhalf) * dx[1] / (prob_hi[1] - prob_lo[1]) - one
                                                 : two * (z - prob_lo[2])  / (prob_hi[2] - prob_lo[2]) - one;
 
            x_vel_pert(i, j, k) = U_0 * (one - y_h * y_h);
 
            if (pert_delta_u != zero) {
                const Real yl = (j + myhalf) * dx[1];
                const Real scaling = std::cos(PI/two * y_h);
                x_vel_pert(i, j, k) += pert_delta_u * scaling * std::cos(aval * yl);
            }
        });
 
        ParallelFor(ybx, [=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept
        {
            const Real* prob_lo = geomdata.ProbLo();
            const Real* prob_hi = geomdata.ProbHi();
            const Real* dx      = geomdata.CellSize();
 
            // Normalized wall-normal dist between -1 and 1
            y_vel_pert(i, j, k) = zero;
 
            const Real z = fourth*( z_nd(i  ,j,k) + z_nd(i  ,j,k+1) + z_nd(i+1,j,k) + z_nd(i+1,j,k+1) );
 
            if (pert_delta_u != zero) {
                const Real xl = (i + myhalf) * dx[0];
                Real y_h = (prob_type == 20) ? two * (j + myhalf) * dx[1] / (prob_hi[1] - prob_lo[1]) - one
                                                     : two * (z - prob_lo[2])  / (prob_hi[2] - prob_lo[2]) - one;
                const Real scaling = std::cos(PI/two * y_h);
                y_vel_pert(i, j, k) += pert_delta_v * scaling * std::cos(bval * xl);
            }
        });
 
        ParallelFor(zbx, [=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept
        {
            z_vel_pert(i, j, k) = zero;
        });
    } // prob_type