diffusive_flux.c

/****************************************************************************
 *                              ArtraCFD                                    *
 *                          <By Huangrui Mo>                                *
 * Copyright (C) Huangrui Mo <huangrui.mo@gmail.com>                        *
 * This file is part of ArtraCFD.                                           *
 * ArtraCFD is free software: you can redistribute it and/or modify it      *
 * under the terms of the GNU General Public License as published by        *
 * the Free Software Foundation, either version 3 of the License, or        *
 * (at your option) any later version.                                      *
 ****************************************************************************/
/****************************************************************************
 * Required Header Files
 ****************************************************************************/
#include "diffusive_flux.h"
#include <string.h> /* manipulating strings */
#include "cfd_commons.h"
#include "commons.h"
/****************************************************************************
 * Function Pointers
 ****************************************************************************/
typedef void (*FvhatReconstructor)(const int, const int, const int, const int,
        const int [restrict], const Real [restrict], const Node *const,
        const Model *, Real [restrict]);
/****************************************************************************
 * Static Function Declarations
 ****************************************************************************/
static void ComputeFvhatX(const int, const int, const int, const int,
        const int [restrict], const Real [restrict], const Node *const,
        const Model *, Real [restrict]);
static void ComputeFvhatY(const int, const int, const int, const int,
        const int [restrict], const Real [restrict], const Node *const,
        const Model *, Real [restrict]);
static void ComputeFvhatZ(const int, const int, const int, const int,
        const int [restrict], const Real [restrict], const Node *const,
        const Model *, Real [restrict]);
/****************************************************************************
 * Global Variables Definition with Private Scope
 ****************************************************************************/
static FvhatReconstructor ReconstructFvhat[DIMS] = {
    ComputeFvhatX,
    ComputeFvhatY,
    ComputeFvhatZ};
/****************************************************************************
 * Function definitions
 ****************************************************************************/
void ComputeFvhat(const int tn, const int s, const int k, const int j, const int i,
        const int partn[restrict], const Real dd[restrict], const Node *const node,
        const Model *model, Real Fvhat[restrict])
{
    const Real zero = 0.0;
    if (zero >= model->refMu) {
        memset(Fvhat, 0, DIMU * sizeof(*Fvhat));
        return;
    }
    ReconstructFvhat[s](tn, k, j, i, partn, dd, node, model, Fvhat);
    return;
}
static void ComputeFvhatX(const int tn, const int k, const int j, const int i,
        const int partn[restrict], const Real dd[restrict], const Node *const node,
        const Model *model, Real Fvhat[restrict])
{
    const int idx = IndexNode(k, j, i, partn[Y], partn[X]);
    const int idxS = IndexNode(k, j - 1, i, partn[Y], partn[X]);
    const int idxN = IndexNode(k, j + 1, i, partn[Y], partn[X]);
    const int idxF = IndexNode(k - 1, j, i, partn[Y], partn[X]);
    const int idxB = IndexNode(k + 1, j, i, partn[Y], partn[X]);

    const int idxE = IndexNode(k, j, i + 1, partn[Y], partn[X]);
    const int idxSE = IndexNode(k, j - 1, i + 1, partn[Y], partn[X]);
    const int idxNE = IndexNode(k, j + 1, i + 1, partn[Y], partn[X]);
    const int idxFE = IndexNode(k - 1, j, i + 1, partn[Y], partn[X]);
    const int idxBE = IndexNode(k + 1, j, i + 1, partn[Y], partn[X]);

    const Real *restrict U = node[idx].U[tn];
    const Real u = U[1] / U[0];
    const Real v = U[2] / U[0];
    const Real w = U[3] / U[0];
    const Real T = ComputeTemperature(model->cv, U);

    U = node[idxS].U[tn];
    const Real uS = U[1] / U[0];
    const Real vS = U[2] / U[0];

    U = node[idxN].U[tn];
    const Real uN = U[1] / U[0];
    const Real vN = U[2] / U[0];

    U = node[idxF].U[tn];
    const Real uF = U[1] / U[0];
    const Real wF = U[3] / U[0];

    U = node[idxB].U[tn];
    const Real uB = U[1] / U[0];
    const Real wB = U[3] / U[0];

    U = node[idxE].U[tn];
    const Real uE = U[1] / U[0];
    const Real vE = U[2] / U[0];
    const Real wE = U[3] / U[0];
    const Real TE = ComputeTemperature(model->cv, U);

    U = node[idxSE].U[tn];
    const Real uSE = U[1] / U[0];
    const Real vSE = U[2] / U[0];

    U = node[idxNE].U[tn];
    const Real uNE = U[1] / U[0];
    const Real vNE = U[2] / U[0];

    U = node[idxFE].U[tn];
    const Real uFE = U[1] / U[0];
    const Real wFE = U[3] / U[0];

    U = node[idxBE].U[tn];
    const Real uBE = U[1] / U[0];
    const Real wBE = U[3] / U[0];

    const Real du_dx = (uE - u) * dd[X];
    const Real dv_dy = 0.25 * (vN + vNE - vS - vSE) * dd[Y];
    const Real dw_dz = 0.25 * (wB + wBE - wF - wFE) * dd[Z];
    const Real du_dy = 0.25 * (uN + uNE - uS - uSE) * dd[Y];
    const Real dv_dx = (vE - v) * dd[X];
    const Real du_dz = 0.25 * (uB + uBE - uF - uFE) * dd[Z];
    const Real dw_dx = (wE - w) * dd[X];
    const Real dT_dx = (TE - T) * dd[X];

    /* calculate interfacial values */
    const Real uhat = 0.5 * (u + uE);
    const Real vhat = 0.5 * (v + vE);
    const Real what = 0.5 * (w + wE);
    const Real That = 0.5 * (T + TE);
    const Real mu = model->refMu * Viscosity(That * model->refT);
    const Real heatK = model->gamma * model->cv * mu / PrandtlNumber();
    const Real divV = du_dx + dv_dy + dw_dz;

    Fvhat[0] = 0.0;
    Fvhat[1] = mu * (du_dx + du_dx - (2.0/3.0) * divV);
    Fvhat[2] = mu * (du_dy + dv_dx);
    Fvhat[3] = mu * (du_dz + dw_dx);
    Fvhat[4] = heatK * dT_dx + Fvhat[1] * uhat + Fvhat[2] * vhat + Fvhat[3] * what;
    return;
}
static void ComputeFvhatY(const int tn, const int k, const int j, const int i,
        const int partn[restrict], const Real dd[restrict], const Node *const node,
        const Model *model, Real Fvhat[restrict])
{
    const int idx = IndexNode(k, j, i, partn[Y], partn[X]);
    const int idxW = IndexNode(k, j, i - 1, partn[Y], partn[X]);
    const int idxE = IndexNode(k, j, i + 1, partn[Y], partn[X]);
    const int idxF = IndexNode(k - 1, j, i, partn[Y], partn[X]);
    const int idxB = IndexNode(k + 1, j, i, partn[Y], partn[X]);

    const int idxN = IndexNode(k, j + 1, i, partn[Y], partn[X]);
    const int idxWN = IndexNode(k, j + 1, i - 1, partn[Y], partn[X]);
    const int idxEN = IndexNode(k, j + 1, i + 1, partn[Y], partn[X]);
    const int idxFN = IndexNode(k - 1, j + 1, i, partn[Y], partn[X]);
    const int idxBN = IndexNode(k + 1, j + 1, i, partn[Y], partn[X]);

    const Real *restrict U = node[idx].U[tn];
    const Real u = U[1] / U[0];
    const Real v = U[2] / U[0];
    const Real w = U[3] / U[0];
    const Real T = ComputeTemperature(model->cv, U);

    U = node[idxW].U[tn];
    const Real uW = U[1] / U[0];
    const Real vW = U[2] / U[0];

    U = node[idxE].U[tn];
    const Real uE = U[1] / U[0];
    const Real vE = U[2] / U[0];

    U = node[idxF].U[tn];
    const Real vF = U[2] / U[0];
    const Real wF = U[3] / U[0];

    U = node[idxB].U[tn];
    const Real vB = U[2] / U[0];
    const Real wB = U[3] / U[0];

    U = node[idxN].U[tn];
    const Real uN = U[1] / U[0];
    const Real vN = U[2] / U[0];
    const Real wN = U[3] / U[0];
    const Real TN = ComputeTemperature(model->cv, U);

    U = node[idxWN].U[tn];
    const Real uWN = U[1] / U[0];
    const Real vWN = U[2] / U[0];

    U = node[idxEN].U[tn];
    const Real uEN = U[1] / U[0];
    const Real vEN = U[2] / U[0];

    U = node[idxFN].U[tn];
    const Real vFN = U[2] / U[0];
    const Real wFN = U[3] / U[0];

    U = node[idxBN].U[tn];
    const Real vBN = U[2] / U[0];
    const Real wBN = U[3] / U[0];

    const Real dv_dx = 0.25 * (vE + vEN - vW - vWN) * dd[X];
    const Real du_dy = (uN - u) * dd[Y];
    const Real dv_dy = (vN - v) * dd[Y];
    const Real du_dx = 0.25 * (uE + uEN - uW - uWN) * dd[X];
    const Real dw_dz = 0.25 * (wB + wBN - wF - wFN) * dd[Z];
    const Real dv_dz = 0.25 * (vB + vBN - vF - vFN) * dd[Z];
    const Real dw_dy = (wN - w) * dd[Y];
    const Real dT_dy = (TN - T) * dd[Y];

    /* calculate interfacial values */
    const Real uhat = 0.5 * (u + uN);
    const Real vhat = 0.5 * (v + vN);
    const Real what = 0.5 * (w + wN);
    const Real That = 0.5 * (T + TN);
    const Real mu = model->refMu * Viscosity(That * model->refT);
    const Real heatK = model->gamma * model->cv * mu / PrandtlNumber();
    const Real divV = du_dx + dv_dy + dw_dz;

    Fvhat[0] = 0.0;
    Fvhat[1] = mu * (dv_dx + du_dy);
    Fvhat[2] = mu * (dv_dy + dv_dy - (2.0/3.0) * divV);
    Fvhat[3] = mu * (dv_dz + dw_dy);
    Fvhat[4] = heatK * dT_dy + Fvhat[1] * uhat + Fvhat[2] * vhat + Fvhat[3] * what;
    return ;
}
static void ComputeFvhatZ(const int tn, const int k, const int j, const int i,
        const int partn[restrict], const Real dd[restrict], const Node *const node,
        const Model *model, Real Fvhat[restrict])
{
    const int idx = IndexNode(k, j, i, partn[Y], partn[X]);
    const int idxW = IndexNode(k, j, i - 1, partn[Y], partn[X]);
    const int idxE = IndexNode(k, j, i + 1, partn[Y], partn[X]);
    const int idxS = IndexNode(k, j - 1, i, partn[Y], partn[X]);
    const int idxN = IndexNode(k, j + 1, i, partn[Y], partn[X]);

    const int idxB = IndexNode(k + 1, j, i, partn[Y], partn[X]);
    const int idxWB = IndexNode(k + 1, j, i - 1, partn[Y], partn[X]);
    const int idxEB = IndexNode(k + 1, j, i + 1, partn[Y], partn[X]);
    const int idxSB = IndexNode(k + 1, j - 1, i, partn[Y], partn[X]);
    const int idxNB = IndexNode(k + 1, j + 1, i, partn[Y], partn[X]);

    const Real *restrict U = node[idx].U[tn];
    const Real u = U[1] / U[0];
    const Real v = U[2] / U[0];
    const Real w = U[3] / U[0];
    const Real T = ComputeTemperature(model->cv, U);

    U = node[idxW].U[tn];
    const Real uW = U[1] / U[0];
    const Real wW = U[3] / U[0];

    U = node[idxE].U[tn];
    const Real uE = U[1] / U[0];
    const Real wE = U[3] / U[0];

    U = node[idxS].U[tn];
    const Real vS = U[2] / U[0];
    const Real wS = U[3] / U[0];

    U = node[idxN].U[tn];
    const Real vN = U[2] / U[0];
    const Real wN = U[3] / U[0];

    U = node[idxB].U[tn];
    const Real uB = U[1] / U[0];
    const Real vB = U[2] / U[0];
    const Real wB = U[3] / U[0];
    const Real TB = ComputeTemperature(model->cv, U);

    U = node[idxWB].U[tn];
    const Real uWB = U[1] / U[0];
    const Real wWB = U[3] / U[0];

    U = node[idxEB].U[tn];
    const Real uEB = U[1] / U[0];
    const Real wEB = U[3] / U[0];

    U = node[idxSB].U[tn];
    const Real vSB = U[2] / U[0];
    const Real wSB = U[3] / U[0];

    U = node[idxNB].U[tn];
    const Real vNB = U[2] / U[0];
    const Real wNB = U[3] / U[0];

    const Real dw_dx = 0.25 * (wE + wEB - wW - wWB) * dd[X];
    const Real du_dz = (uB - u) * dd[Z];
    const Real dw_dy = 0.25 * (wN + wNB - wS - wSB) * dd[Y];
    const Real dv_dz = (vB - v) * dd[Z];
    const Real du_dx = 0.25 * (uE + uEB - uW - uWB) * dd[X];
    const Real dv_dy = 0.25 * (vN + vNB - vS - vSB) * dd[Y];
    const Real dw_dz = (wB - w) * dd[Z];
    const Real dT_dz = (TB - T) * dd[Z];

    /* calculate interfacial values */
    const Real uhat = 0.5 * (u + uB);
    const Real vhat = 0.5 * (v + vB);
    const Real what = 0.5 * (w + wB);
    const Real That = 0.5 * (T + TB);
    const Real mu = model->refMu * Viscosity(That * model->refT);
    const Real heatK = model->gamma * model->cv * mu / PrandtlNumber();
    const Real divV = du_dx + dv_dy + dw_dz;

    Fvhat[0] = 0.0;
    Fvhat[1] = mu * (dw_dx + du_dz);
    Fvhat[2] = mu * (dw_dy + dv_dz);
    Fvhat[3] = mu * (dw_dz + dw_dz - (2.0/3.0) * divV);
    Fvhat[4] = heatK * dT_dz + Fvhat[1] * uhat + Fvhat[2] * vhat + Fvhat[3] * what;
    return;
}
/* a good practice: end file with a newline */