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WIP: FV::Div_a_Grad_perp operator #2823

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WIP: FV::Div_a_Grad_perp operator #2823

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84 changes: 46 additions & 38 deletions src/mesh/fv_ops.cxx
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Original file line number Diff line number Diff line change
Expand Up @@ -51,11 +51,15 @@ Field3D Div_a_Grad_perp(const Field3D& a, const Field3D& f) {
for (int k = 0; k < mesh->LocalNz; k++) {
// Calculate flux from i to i+1

BoutReal fout = 0.5 * (a(i, j, k) + a(i + 1, j, k))
* (coord->J(i, j, k) * coord->g11(i, j, k)
+ coord->J(i + 1, j, k) * coord->g11(i + 1, j, k))
* (f(i + 1, j, k) - f(i, j, k))
/ (coord->dx(i, j, k) + coord->dx(i + 1, j, k));
BoutReal fout =
0.5
* (a(i, j, k) + a(i + 1, j, k))
// Average <J g^{xx} / dx>
* 0.5
* (coord->J(i, j, k) * coord->g11(i, j, k) / coord->dx(i, j, k)
+ coord->J(i + 1, j, k) * coord->g11(i + 1, j, k) / coord->dx(i + 1, j, k))
// X derivative at X boundary
* (f(i + 1, j, k) - f(i, j, k));

result(i, j, k) += fout / (coord->dx(i, j, k) * coord->J(i, j, k));
result(i + 1, j, k) -= fout / (coord->dx(i + 1, j, k) * coord->J(i + 1, j, k));
Expand Down Expand Up @@ -106,44 +110,48 @@ Field3D Div_a_Grad_perp(const Field3D& a, const Field3D& f) {
auto ikp = i.zp();
auto ikm = i.zm();
{
const BoutReal coef = 0.5
* (g_23.c[i] / SQ(J.c[i] * Bxy.c[i])
+ g_23.up[i.yp()] / SQ(J.up[i.yp()] * Bxy.up[i.yp()]));

// Calculate Z derivative at y boundary
const BoutReal dfdz = 0.5
* (f_slice.c[ikp] - f_slice.c[ikm] + f_slice.up[ikp.yp()]
- f_slice.up[ikm.yp()])
/ (dz.c[i] + dz.up[i.yp()]);

// Y derivative
const BoutReal dfdy =
2. * (f_slice.up[i.yp()] - f_slice.c[i]) / (dy.up[i.yp()] + dy.c[i]);

const BoutReal fout = 0.25 * (a_slice.c[i] + a_slice.up[i.yp()])
* (J.c[i] * g23.c[i] + J.up[i.yp()] * g23.up[i.yp()])
* (dfdz - coef * dfdy);
const BoutReal fout =
0.5 * (a_slice.c[i] + a_slice.up[i.yp()])
* (
// Average <J g^{yz} / dz>
0.5
* (J.c[i] * g23.c[i] / dz.c[i]
+ J.up[i.yp()] * g23.up[i.yp()] / dz.up[i.yp()])
// Z derivative at y boundary
* 0.25
* (f_slice.c[ikp] - f_slice.c[ikm] + f_slice.up[ikp.yp()]
- f_slice.up[ikm.yp()])
// Average <J g^{yz} g_{yz} / (g_{yy} dy)>
- 0.5
* (J.c[i] * g23.c[i] * g_23.c[i] / (SQ(J.c[i] * Bxy.c[i]) * dy.c[i])
+ J.up[i.yp()] * g23.up[i.yp()] * g_23.up[i.yp()]
/ (SQ(J.up[i.yp()] * Bxy.up[i.yp()]) * dy.up[i.yp()]))
// Y derivative at Y boundary
* (f_slice.up[i.yp()] - f_slice.c[i]));

yzresult[i] += fout / (dy.c[i] * J.c[i]);
}
{
// Calculate flux between j and j-1
const BoutReal coef =
0.5
* (g_23.c[i] / SQ(J.c[i] * Bxy.c[i])
+ g_23.down[i.ym()] / SQ(J.down[i.ym()] * Bxy.down[i.ym()]));

const BoutReal dfdz = 0.5
* (f_slice.c[ikp] - f_slice.c[ikm] + f_slice.down[ikp.ym()]
- f_slice.down[ikm.ym()])
/ (dz.c[i] + dz.down[i.ym()]);

const BoutReal dfdy =
2. * (f_slice.c[i] - f_slice.down[i.ym()]) / (dy.c[i] + dy.down[i.ym()]);

const BoutReal fout = 0.25 * (a_slice.c[i] + a_slice.down[i.ym()])
* (J.c[i] * g23.c[i] + J.down[i.ym()] * g23.down[i.ym()])
* (dfdz - coef * dfdy);

const BoutReal fout =
0.5 * (a_slice.c[i] + a_slice.down[i.ym()])
* (
// Average <J g^{yz} / dz>
0.5
* (J.c[i] * g23.c[i] / dz.c[i]
+ J.down[i.ym()] * g23.down[i.ym()] / dz.down[i.ym()])
// Z derivative at y boundary
* 0.25
* (f_slice.c[ikp] - f_slice.c[ikm] + f_slice.down[ikp.ym()]
- f_slice.down[ikm.ym()])
// Average <J g^{yz} g_{yz} / (g_{yy} dy)>
- 0.5
* (J.c[i] * g23.c[i] * g_23.c[i] / (SQ(J.c[i] * Bxy.c[i]) * dy.c[i])
+ J.down[i.ym()] * g23.down[i.ym()] * g_23.down[i.ym()]
/ (SQ(J.down[i.ym()] * Bxy.down[i.ym()]) * dy.down[i.ym()]))
// Y derivative at Y boundary
* (f_slice.c[i] - f_slice.down[i.ym()]));

yzresult[i] -= fout / (dy.c[i] * J.c[i]);
}
Expand Down
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