embedded3 item 9b: the device step carries a static cut-cell mask (e3_cut.cu: cut predictor, apertured merged continuity with the fold, owner-read corrections; device CG off-stencil links) — host = device to 2e-10 (CFD1 cylinder nz 4) and 4e-14 (sphere) under tight tolerances

Co-Authored-By: Claude Fable 5.1 <[email protected]>
2026-09-17 17:22:52 -05:00
parent 0fa05f2056
commit 3b3d6c84c0
8 changed files with 982 additions and 3 deletions
@@ -0,0 +1,309 @@
+/**
+ * embedded3 item 9b: the apertured cut-cell wall's maps on the device — the
+ * host `step/cut_predictor.rs` and `cutwall.rs` expression for expression
+ * (FMA contraction off): the predictor on the open faces of one component
+ * (the momentum volume `V_u = α h A`, mass fluxes averaged from the two
+ * cells, upwind + TVD, apertured diffusion, the projection's pressure
+ * force, the net mass flux times the face's value, the implicit wall
+ * shear, the inertia floor), the apertured continuity with the wall flux
+ * and the fold of the virtually merged small cells into their masters,
+ * the corrections on the open faces reading the owner's p', the pressure
+ * update. Static bodies (the tables are built once).
+ *
+ * Appended after `e3_step.cu` at load (shares E3Params / E3Ptrs and the
+ * helpers there).
+ */
+#define CUT_INERTIA_FLOOR 0.1
+#define CUT_DISTANCE_FLOOR 0.05
+
+struct E3Cut {
+    const double *a_u, *a_v, *a_w;      /* apertures per face */
+    const double *d_u, *d_v, *d_w;      /* φ at the face centres */
+    const double *ub_u, *ub_v, *ub_w;   /* surface velocity component at the foot per face */
+    const double *wall_flux;            /* per cell, compatible */
+    const int *open_u, *open_v, *open_w;/* unknown faces */
+    const int *active;                  /* cells with an equation */
+    const unsigned int *owner;          /* the master of a merged cell (itself otherwise) */
+    const unsigned int *fold_ptr, *fold_idx; /* CSR: the slaves of every cell */
+    double *cell_flux;                  /* scratch per cell */
+};
+
+/* Face index of component c at lattice (i, j, k); −1 outside (z wraps when periodic). */
+__device__ __forceinline__ int cut_face(const E3Params& g, int c, int i, int j, int k)
+{
+    int ni = c == 0 ? g.nx + 1 : g.nx;
+    int nj = c == 1 ? g.ny + 1 : g.ny;
+    int nk = c == 2 ? g.nz + 1 : g.nz;
+    if (i < 0 || i >= ni || j < 0 || j >= nj) return -1;
+    if (g.periodic_z) { k = ((k % g.nz) + g.nz) % g.nz; }
+    else if (k < 0 || k >= nk) return -1;
+    if (c == 0) return (k * g.ny + j) * (g.nx + 1) + i;
+    if (c == 1) return (k * (g.ny + 1) + j) * g.nx + i;
+    return (k * g.ny + j) * g.nx + i;
+}
+
+__device__ __forceinline__ int cut_cell(const E3Params& g, int i, int j, int k)
+{
+    if (i < 0 || i >= g.nx || j < 0 || j >= g.ny) return -1;
+    if (g.periodic_z) { k = ((k % g.nz) + g.nz) % g.nz; }
+    else if (k < 0 || k >= g.nz) return -1;
+    return (k * g.ny + j) * g.nx + i;
+}
+
+__device__ __forceinline__ const double* cut_ap(const E3Cut& m, int c) { return c == 0 ? m.a_u : (c == 1 ? m.a_v : m.a_w); }
+__device__ __forceinline__ const double* cut_old(const E3Ptrs& f, int c) { return c == 0 ? f.uo : (c == 1 ? f.vo : f.wo); }
+
+/* Aperture of component `cc` at the lattice point, or `dflt` outside. */
+__device__ __forceinline__ double cut_ap_at(const E3Params& g, const E3Cut& m, int cc, int i, int j, int k, double dflt)
+{
+    int fidx = cut_face(g, cc, i, j, k);
+    return fidx < 0 ? dflt : cut_ap(m, cc)[fidx];
+}
+
+/* The predicted value of the open face of component c at (i, j, k). */
+__device__ double cut_face_update(const E3Params& g, const E3Ptrs& f, const E3Cut& m, int c, int i, int j, int k, int fidx)
+{
+    double h[3] = { g.dx, g.dy, g.dz };
+    double n[3] = { (double)g.nx, (double)g.ny, (double)g.nz };
+    double area[3] = { g.dy * g.dz, g.dx * g.dz, g.dx * g.dy };
+    double rho = g.rho, mu = g.nu * g.rho;
+    int sides[3][2] = { { g.bx0, g.bx1 }, { g.by0, g.by1 }, { g.bz0, g.bz1 } };
+    int p[3] = { i, j, k };
+    const double* old_c = cut_old(f, c);
+    double u0 = old_c[fidx];
+    /* the control volume's geometry (cutwall.rs cv_geometry) */
+    double alpha = cut_ap(m, c)[fidx];
+    double apm[3], app[3];
+    int cm[3] = { i, j, k }; cm[c] -= 1;   /* cell minus */
+    int cp[3] = { i, j, k };               /* cell plus */
+    for (int d = 0; d < 3; ++d) {
+        if (d == c) {
+            int qm[3] = { i, j, k }; qm[c] -= 1;
+            int qp[3] = { i, j, k }; qp[c] += 1;
+            double am = cut_ap_at(g, m, c, qm[0], qm[1], qm[2], alpha);
+            double apl = cut_ap_at(g, m, c, qp[0], qp[1], qp[2], alpha);
+            apm[d] = 0.5 * (am + alpha);
+            app[d] = 0.5 * (alpha + apl);
+        } else {
+            int q1[3] = { cm[0], cm[1], cm[2] }; q1[d] += 1;
+            int q2[3] = { cp[0], cp[1], cp[2] }; q2[d] += 1;
+            apm[d] = 0.5 * (cut_ap_at(g, m, d, cm[0], cm[1], cm[2], 1.0) + cut_ap_at(g, m, d, cp[0], cp[1], cp[2], 1.0));
+            app[d] = 0.5 * (cut_ap_at(g, m, d, q1[0], q1[1], q1[2], 1.0) + cut_ap_at(g, m, d, q2[0], q2[1], q2[2], 1.0));
+        }
+    }
+    double wall[3];
+    for (int d = 0; d < 3; ++d) wall[d] = -(app[d] - apm[d]) * area[d];
+    double h_min = fmin(fmin(g.dx, g.dy), g.dz);
+    const double* dist = c == 0 ? m.d_u : (c == 1 ? m.d_v : m.d_w);
+    double distance = fmax(dist[fidx] + 0.5 * h[c] * (1.0 - alpha), CUT_DISTANCE_FLOOR * h_min);
+    const double* ubt = c == 0 ? m.ub_u : (c == 1 ? m.ub_v : m.ub_w);
+    double ub = ubt[fidx];
+    /* face position */
+    double x[3];
+    for (int d = 0; d < 3; ++d) x[d] = (p[d] + (d == c ? 0.0 : 0.5)) * h[d];
+
+    double mass_out = 0.0, conv = 0.0, diff = 0.0;
+    for (int d = 0; d < 3; ++d) {
+        double a_d = area[d];
+        int q[3];
+        /* neighbouring faces of this component along d */
+        q[0] = i; q[1] = j; q[2] = k; q[d] += 1;  int f_up1 = cut_face(g, c, q[0], q[1], q[2]);
+        q[0] = i; q[1] = j; q[2] = k; q[d] += 2;  int f_up2 = cut_face(g, c, q[0], q[1], q[2]);
+        q[0] = i; q[1] = j; q[2] = k; q[d] -= 1;  int f_dn1 = cut_face(g, c, q[0], q[1], q[2]);
+        q[0] = i; q[1] = j; q[2] = k; q[d] -= 2;  int f_dn2 = cut_face(g, c, q[0], q[1], q[2]);
+        double up1 = f_up1 >= 0 ? old_c[f_up1] : 0.0;
+        double up2 = f_up2 >= 0 ? old_c[f_up2] : 0.0;
+        double dn1 = f_dn1 >= 0 ? old_c[f_dn1] : 0.0;
+        double dn2 = f_dn2 >= 0 ? old_c[f_dn2] : 0.0;
+        double m_plus, m_minus;
+        if (d == c) {
+            double f_up = (f_up1 >= 0 ? cut_ap(m, c)[f_up1] : alpha) * (f_up1 >= 0 ? up1 : u0);
+            double f_dn = (f_dn1 >= 0 ? cut_ap(m, c)[f_dn1] : alpha) * (f_dn1 >= 0 ? dn1 : u0);
+            double f0 = alpha * u0;
+            m_plus = 0.5 * (f0 + f_up) * a_d;
+            m_minus = 0.5 * (f_dn + f0) * a_d;
+        } else {
+            const double* old_d = cut_old(f, d);
+            int q1[3] = { cm[0], cm[1], cm[2] }; q1[d] += 1;
+            int q2[3] = { cp[0], cp[1], cp[2] }; q2[d] += 1;
+            int fa = cut_face(g, d, q1[0], q1[1], q1[2]);
+            int fb = cut_face(g, d, q2[0], q2[1], q2[2]);
+            int fc = cut_face(g, d, cm[0], cm[1], cm[2]);
+            int fd = cut_face(g, d, cp[0], cp[1], cp[2]);
+            double fla = fa >= 0 ? cut_ap(m, d)[fa] * old_d[fa] : 0.0;
+            double flb = fb >= 0 ? cut_ap(m, d)[fb] * old_d[fb] : 0.0;
+            double flc = fc >= 0 ? cut_ap(m, d)[fc] * old_d[fc] : 0.0;
+            double fld = fd >= 0 ? cut_ap(m, d)[fd] * old_d[fd] : 0.0;
+            m_plus = 0.5 * (fla + flb) * a_d;
+            m_minus = 0.5 * (flc + fld) * a_d;
+        }
+        mass_out += m_plus - m_minus;
+        /* beyond a domain side along d */
+        double beyond_p = u0, beyond_m = u0;
+        if (sides[d][1] == SIDE_VELOCITY || sides[d][0] == SIDE_VELOCITY) {
+            /* the boundary tables: [side][component] at the face's transverse position */
+            const double* tp = 0; const double* tm = 0; int idx_p = 0, idx_m = 0;
+            if (d == 0) { tp = c == 0 ? f.bx1u : (c == 1 ? f.bx1v : f.bx1w); tm = c == 0 ? f.bx0u : (c == 1 ? f.bx0v : f.bx0w);
+                          int nj = c == 1 ? g.ny + 1 : g.ny; idx_p = idx_m = k * nj + j; }
+            else if (d == 1) { tp = c == 0 ? f.by1u : (c == 1 ? f.by1v : f.by1w); tm = c == 0 ? f.by0u : (c == 1 ? f.by0v : f.by0w);
+                          int ni = c == 0 ? g.nx + 1 : g.nx; idx_p = idx_m = k * ni + i; }
+            else { tp = c == 0 ? f.bz1u : (c == 1 ? f.bz1v : f.bz1w); tm = c == 0 ? f.bz0u : (c == 1 ? f.bz0v : f.bz0w);
+                          int ni = c == 0 ? g.nx + 1 : g.nx; idx_p = idx_m = j * ni + i; }
+            if (sides[d][1] == SIDE_VELOCITY) beyond_p = tp[idx_p];
+            if (sides[d][0] == SIDE_VELOCITY) beyond_m = tm[idx_m];
+        }
+        (void)n; (void)x;
+        /* convection through the plus face */
+        double u_plus, delta_plus;
+        if (f_up1 >= 0) {
+            if (g.scheme == SCHEME_UPWIND) delta_plus = 0.0;
+            else if (m_plus >= 0.0) delta_plus = face_corr3(g.scheme, f_dn1 >= 0, dn1, u0, up1);
+            else delta_plus = face_corr3(g.scheme, f_up2 >= 0, up2, up1, u0);
+            u_plus = upwind3(m_plus, u0, up1);
+        } else { u_plus = upwind3(m_plus, u0, beyond_p); delta_plus = 0.0; }
+        double u_minus, delta_minus;
+        if (f_dn1 >= 0) {
+            if (g.scheme == SCHEME_UPWIND) delta_minus = 0.0;
+            else if (m_minus >= 0.0) delta_minus = face_corr3(g.scheme, f_dn2 >= 0, dn2, dn1, u0);
+            else delta_minus = face_corr3(g.scheme, f_up1 >= 0, up1, u0, dn1);
+            u_minus = upwind3(m_minus, dn1, u0);
+        } else { u_minus = upwind3(m_minus, beyond_m, u0); delta_minus = 0.0; }
+        conv += m_plus * (u_plus + delta_plus) - m_minus * (u_minus + delta_minus);
+        /* diffusion */
+        double g_minus = apm[d], g_plus = app[d];
+        if (f_up1 >= 0) diff += mu * g_plus * a_d * (up1 - u0) / h[d];
+        else if (sides[d][1] == SIDE_VELOCITY) diff += mu * g_plus * a_d * (beyond_p - u0) / (0.5 * h[d]);
+        if (f_dn1 >= 0) diff -= mu * g_minus * a_d * (u0 - dn1) / h[d];
+        else if (sides[d][0] == SIDE_VELOCITY) diff -= mu * g_minus * a_d * (u0 - beyond_m) / (0.5 * h[d]);
+    }
+    conv -= mass_out * u0;
+    int cpi = cut_cell(g, cp[0], cp[1], cp[2]);
+    int cmi = cut_cell(g, cm[0], cm[1], cm[2]);
+    double p_plus = cpi >= 0 ? f.p[cpi] : 0.0;
+    double p_minus = cmi >= 0 ? f.p[cmi] : 0.0;
+    double pressure = -(p_plus - p_minus) * alpha * area[c];
+    double v_u = alpha * h[c] * area[c];
+    const double* src = c == 0 ? f.su : (c == 1 ? f.sv : f.sw);
+    double source = src[fidx] * v_u;
+    double a_w = sqrt(wall[0] * wall[0] + wall[1] * wall[1] + wall[2] * wall[2]);
+    double shear = mu * a_w / distance;
+    double v_eff = fmax(alpha, CUT_INERTIA_FLOOR) * h[c] * area[c];
+    double inertia = rho * v_eff / g.dt;
+    return (inertia * u0 - conv + diff + pressure + source + shear * ub) / (inertia + shear);
+}
+
+/* The predictor on the open interior faces of component c. */
+extern "C" __global__ void e3_cut_predict(E3Params g, E3Ptrs f, E3Cut m, int c)
+{
+    int t = blockIdx.x * blockDim.x + threadIdx.x;
+    int ni = c == 0 ? g.nx + 1 : g.nx;
+    int nj = c == 1 ? g.ny + 1 : g.ny;
+    int nk = c == 2 ? g.nz + 1 : g.nz;
+    if (t >= ni * nj * nk) return;
+    int i = t % ni; int j = (t / ni) % nj; int k = t / (ni * nj);
+    if (c == 0 && (i == 0 || i == g.nx)) return;
+    if (c == 1 && (j == 0 || j == g.ny)) return;
+    if (c == 2) { if (g.periodic_z) { if (k == g.nz) return; } else if (k == 0 || k == g.nz) return; }
+    const int* open = c == 0 ? m.open_u : (c == 1 ? m.open_v : m.open_w);
+    if (!open[t]) return;
+    double val = cut_face_update(g, f, m, c, i, j, k, t);
+    double* out = c == 0 ? f.u : (c == 1 ? f.v : f.w);
+    out[t] = val;
+}
+
+/* cell_flux = ρ (Σ apertured flux out + wall flux) on the active cells (0 elsewhere). */
+extern "C" __global__ void e3_cut_divergence(E3Params g, E3Ptrs f, E3Cut m, int starred)
+{
+    int t = blockIdx.x * blockDim.x + threadIdx.x;
+    int total = g.nx * g.ny * g.nz;
+    if (t >= total) return;
+    if (!m.active[t]) { m.cell_flux[t] = 0.0; return; }
+    int i = t % g.nx; int j = (t / g.nx) % g.ny; int k = t / (g.nx * g.ny);
+    const double* u = starred ? f.us : f.u;
+    const double* v = starred ? f.vs : f.v;
+    const double* w = starred ? f.ws : f.w;
+    int ue = uf3(g, k, j, i + 1), uw = uf3(g, k, j, i);
+    int vn = vf3(g, k, j + 1, i), vs = vf3(g, k, j, i);
+    int wt = wf3(g, k + 1, j, i), wb = wf3(g, k, j, i);
+    double divergence_flux = g.rho
+        * ((m.a_u[ue] * u[ue] - m.a_u[uw] * u[uw]) * (g.dy * g.dz)
+           + (m.a_v[vn] * v[vn] - m.a_v[vs] * v[vs]) * (g.dx * g.dz)
+           + (m.a_w[wt] * w[wt] - m.a_w[wb] * w[wb]) * (g.dx * g.dy));
+    divergence_flux += g.rho * m.wall_flux[t];
+    m.cell_flux[t] = divergence_flux;
+}
+
+/* The merged fluxes: sp = −(own + slaves) on the owning cells when `write_sp`;
+ * partial[block] = Σ |merged flux| (the source scale / the mass imbalance). */
+extern "C" __global__ void e3_cut_fold(E3Params g, E3Ptrs f, E3Cut m, int write_sp, double* __restrict__ partial)
+{
+    int t = blockIdx.x * blockDim.x + threadIdx.x;
+    int total = g.nx * g.ny * g.nz;
+    double v = 0.0;
+    if (t < total) {
+        if (m.active[t] && m.owner[t] == (unsigned int)t) {
+            double s = m.cell_flux[t];
+            for (unsigned int l = m.fold_ptr[t]; l < m.fold_ptr[t + 1]; ++l) s += m.cell_flux[m.fold_idx[l]];
+            if (write_sp) f.sp[t] = -s;
+            v = fabs(s);
+        } else if (write_sp) {
+            f.sp[t] = 0.0;
+        }
+    }
+    __shared__ double sh[256];
+    sh[threadIdx.x] = v;
+    __syncthreads();
+    for (int s = 128; s > 0; s >>= 1) { if (threadIdx.x < s) sh[threadIdx.x] += sh[threadIdx.x + s]; __syncthreads(); }
+    if (threadIdx.x == 0) partial[blockIdx.x] = sh[0];
+}
+
+/* The corrections on the open interior faces of component c from the owners' p'. */
+extern "C" __global__ void e3_cut_correct(E3Params g, E3Ptrs f, E3Cut m, int c)
+{
+    int t = blockIdx.x * blockDim.x + threadIdx.x;
+    int ni = c == 0 ? g.nx + 1 : g.nx;
+    int nj = c == 1 ? g.ny + 1 : g.ny;
+    int nk = c == 2 ? g.nz + 1 : g.nz;
+    if (t >= ni * nj * nk) return;
+    int i = t % ni; int j = (t / ni) % nj; int k = t / (ni * nj);
+    double cc = g.dt / g.rho;
+    const int* open = c == 0 ? m.open_u : (c == 1 ? m.open_v : m.open_w);
+    double* out = c == 0 ? f.u : (c == 1 ? f.v : f.w);
+    const double* star = c == 0 ? f.us : (c == 1 ? f.vs : f.ws);
+    int interior = c == 0 ? (i >= 1 && i < g.nx) : (c == 1 ? (j >= 1 && j < g.ny)
+                 : (g.periodic_z ? (k < g.nz) : (k >= 1 && k < g.nz)));
+    if (interior) {
+        if (!open[t]) return;
+        int cp[3] = { i, j, k }, cm[3] = { i, j, k }; cm[c] -= 1;
+        int a = cut_cell(g, cp[0], cp[1], cp[2]);
+        int b = cut_cell(g, cm[0], cm[1], cm[2]);
+        double h = c == 0 ? g.dx : (c == 1 ? g.dy : g.dz);
+        double dp = (f.pp[m.owner[a]] - f.pp[m.owner[b]]) / h;
+        out[t] = star[t] - cc * dp;
+        return;
+    }
+    /* outlet faces against 0 outside (no body reaches an outlet) */
+    int s0 = c == 0 ? g.bx0 : (c == 1 ? g.by0 : g.bz0);
+    int s1 = c == 0 ? g.bx1 : (c == 1 ? g.by1 : g.bz1);
+    int own = c == 0 ? i : (c == 1 ? j : k);
+    int nn = c == 0 ? g.nx : (c == 1 ? g.ny : g.nz);
+    double h = c == 0 ? g.dx : (c == 1 ? g.dy : g.dz);
+    if (own == 0 && s0 == SIDE_OUTLET) {
+        int cp[3] = { i, j, k };
+        int a = cut_cell(g, cp[0], cp[1], cp[2]);
+        out[t] = star[t] - cc * (f.pp[a] - 0.0) / (0.5 * h);
+    } else if (own == nn && s1 == SIDE_OUTLET) {
+        int cm[3] = { i, j, k }; cm[c] -= 1;
+        int b = cut_cell(g, cm[0], cm[1], cm[2]);
+        out[t] = star[t] - cc * (0.0 - f.pp[b]) / (0.5 * h);
+    }
+}
+
+/* p += p'(owner) on the active cells. */
+extern "C" __global__ void e3_cut_add_p(E3Params g, E3Ptrs f, E3Cut m)
+{
+    int t = blockIdx.x * blockDim.x + threadIdx.x;
+    if (t >= g.nx * g.ny * g.nz) return;
+    if (!m.active[t]) return;
+    f.p[t] += f.pp[m.owner[t]];
+}