test_poiseuille_ibm.cpp

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// Validation of the assembled IBM velocity solve (the verify_poiseuille_sdflow physics): plane
// Poiseuille through an SDF-defined channel with cut-cell IBM no-slip walls, body-force driven,
// physical units (rho/mu/dt). Solve the backward-Euler x-momentum to steady with the IBM-modified
// stencil and compare to U_max = F*H^2/(8*mu). Exercises buildIbmOverlay + ibmBuildDiffusion +
// ibmModifyStencil + ibmSolidMask + ibmRbgsSweep assembled together. Runs on any Kokkos backend.
#include <cmath>
#include <cstdio>
#include <Kokkos_Core.hpp>
#include <vector>
 
#include "mac_ibm.hpp"
 
using namespace peclet::flow;
 
int main(int argc, char** argv) {
  Kokkos::initialize(argc, argv);
  int status = 0;
  {
    const int g = 1;
    const int nx = 4, nz = 4, ny = 48;  // periodic x (flow) & z; channel along y
    // Half-integer wall positions so the SDF zero lies BETWEEN cells -> fluid cells with solid
    // neighbours (cut cells) form, exercising the Robust-Scaled cut-cell no-slip (not just
    // masking).
    const double ylo = 6.5, yhi = ny - 6.5;  // immersed walls; H = yhi - ylo
    const double H = yhi - ylo;
    const double rho = 1.0, mu = 0.1, dt = 50.0, F = 0.01;
    const double idiag = rho / dt, beta = mu;
    C3 e{nx + 2 * g, ny + 2 * g, nz + 2 * g};
    const std::size_t n = (std::size_t)e.x * e.y * e.z;
    const Off3 offU{-0.5f, 0.0f, 0.0f};  // u stored at the -x face
 
    // channel SDF: sdf(iy) = min(iy - ylo, yhi - iy) (>0 in fluid, <0 in the wall) at each ext
    // cell.
    CCField sdf("sdf", n);
    {
      auto h = Kokkos::create_mirror_view(sdf);
      for (int z = 0; z < e.z; ++z)
        for (int y = 0; y < e.y; ++y)
          for (int x = 0; x < e.x; ++x) {
            int iy = y - g;
            double s = std::min((double)iy - ylo, yhi - (double)iy);
            h((long)x + (long)y * e.x + (long)z * (long)e.x * e.y) = s;
          }
      Kokkos::deep_copy(sdf, h);
    }
 
    // build the u-component IBM overlay
    const int maxCut = (int)((long)nx * ny * nz);
    IbmOverlay ov{Kokkos::View<int*, CCMem>("ci", maxCut),
                  Kokkos::View<int*, CCMem>("nb", maxCut),
                  Kokkos::View<float*, CCMem>("dr", maxCut),
                  Kokkos::View<int*, CCMem>("dc", (std::size_t)maxCut * 6),
                  Kokkos::View<float*, CCMem>("K", (std::size_t)maxCut * 6),
                  Kokkos::View<float*, CCMem>("M", (std::size_t)maxCut * 6),
                  Kokkos::View<float*, CCMem>("X", (std::size_t)maxCut * 6),
                  Kokkos::View<float*, CCMem>("Nbc", (std::size_t)maxCut * 6),
                  Kokkos::View<float*, CCMem>("R", (std::size_t)maxCut * 6)};
    Kokkos::View<int*, CCMem> idMap("idMap", n);
    Kokkos::View<int, CCMem> counter("counter");
    int nCut =
        buildIbmOverlay<1>(CCConst(sdf), e, g, offU, /*bc_type Dirichlet*/ 0, ov, idMap, counter);
 
    // base diffusion stencil + apply overlay
    using FV = Kokkos::View<float*, CCMem>;
    FV AC("AC", n), AW("AW", n), AE("AE", n), AS("AS", n), AN("AN", n), AB("AB", n), AT("AT", n);
    Kokkos::View<double*, CCMem> inhom("inhom", n), rscale("rscale", n);
    Kokkos::deep_copy(rscale, 1.0);  // non-cut cells: scale 1
    ibmBuildDiffusion(AC, AW, AE, AS, AN, AB, AT, e.x, e.y, e.z, beta, idiag);
    ibmModifyStencil(AC, AW, AE, AS, AN, AB, AT, inhom, rscale, ov, nCut, /*u_bc*/ 0.0f);
 
    // solid mask for u
    CCField mask("mask", n);
    ibmSolidMask(mask, CCConst(sdf), e, offU);
 
    CCField u("u", n), b("b", n);
    Kokkos::deep_copy(u, 0.0);
    CCExec space;
 
    // periodic x,z ghost fill (y handled by the immersed walls / mask)
    auto fillXZ = [&]() {
      CCField uu = u;
      const int Nx = nx, Nz = nz;
      Kokkos::parallel_for(
          "fx", Kokkos::MDRangePolicy<CCExec, Kokkos::Rank<2>>(space, {0, 0}, {e.y, e.z}),
          KOKKOS_LAMBDA(int y, int z) {
            long base = (long)y * e.x + (long)z * (long)e.x * e.y;
            for (int gl = 0; gl < g; ++gl) {
              uu(base + gl) = uu(base + gl + Nx);
              uu(base + g + Nx + gl) = uu(base + g + gl);
            }
          });
      Kokkos::parallel_for(
          "fz", Kokkos::MDRangePolicy<CCExec, Kokkos::Rank<2>>(space, {0, 0}, {e.x, e.y}),
          KOKKOS_LAMBDA(int x, int y) {
            long base = (long)x + (long)y * e.x;
            long sz = (long)e.x * e.y;
            for (int gl = 0; gl < g; ++gl) {
              uu(base + (long)gl * sz) = uu(base + (long)(gl + Nz) * sz);
              uu(base + (long)(g + Nz + gl) * sz) = uu(base + (long)(g + gl) * sz);
            }
          });
      space.fence();
    };
 
    // time-step the IBM momentum solve to steady state (slow approach: ~mu*k^2*dt per step)
    for (int step = 0; step < 600; ++step) {
      // RHS b' = rscale * (idiag*u + F)   (Robust-Scaled; inhom=0 for no-slip walls)
      {
        CCField uu = u, bb = b;
        auto rs = rscale;
        double id = idiag, ff = F;
        Kokkos::parallel_for(
            "rhs", Kokkos::RangePolicy<CCExec>(space, 0, n),
            KOKKOS_LAMBDA(std::size_t i) { bb(i) = rs(i) * (id * uu(i) + ff); });
        space.fence();
      }
      for (int it = 0; it < 200; ++it) {
        fillXZ();
        ibmRbgsStencilColor(u, CCConst(b), MConst(AC), MConst(AW), MConst(AE), MConst(AS),
                            MConst(AN), MConst(AB), MConst(AT), CCConst(mask), e, C3{0, 0, 0}, g,
                            0);
        fillXZ();
        ibmRbgsStencilColor(u, CCConst(b), MConst(AC), MConst(AW), MConst(AE), MConst(AS),
                            MConst(AN), MConst(AB), MConst(AT), CCConst(mask), e, C3{0, 0, 0}, g,
                            1);
      }
    }
 
    // extract centerline profile u(y) at x=g,z=g and compare to the parabola
    auto hu = Kokkos::create_mirror_view(u);
    Kokkos::deep_copy(hu, u);
    const double Uana = F * H * H / (8.0 * mu);
    double umax = 0, l2num = 0, l2den = 0;
    for (int iy = 0; iy < ny; ++iy) {
      long i = (long)g + (long)(iy + g) * e.x + (long)g * (long)e.x * e.y;
      double un = hu(i);
      umax = std::fmax(umax, un);
      if (iy > ylo && iy < yhi) {  // fluid interior
        double yy = iy;
        double ue = (F / (2.0 * mu)) * (yy - ylo) * (yhi - yy);
        l2num += (un - ue) * (un - ue);
        l2den += ue * ue;
      }
    }
    const double l2err = std::sqrt(l2num / l2den);
    const double umaxErr = std::fabs(umax - Uana) / Uana;
    std::printf(
        "[poiseuille_ibm] cut cells=%d; U_max=%.5f analytic=%.5f (err %.2e); profile L2 err=%.2e\n",
        nCut, umax, Uana, umaxErr, l2err);
    if (nCut <= 0) {
      std::fprintf(stderr, "FAIL: no cut cells found\n");
      status = 1;
    }
    if (umaxErr > 3e-2) {
      std::fprintf(stderr, "FAIL: U_max off analytic\n");
      status = 1;
    }
    if (l2err > 3e-2) {
      std::fprintf(stderr, "FAIL: profile not parabolic\n");
      status = 1;
    }
    if (!status)
      std::printf("[poiseuille_ibm] PASS: IBM cut-cell channel reproduces Poiseuille (exec %s)\n",
                  Kokkos::DefaultExecutionSpace::name());
  }
  Kokkos::finalize();
  return status;
}