Omar SobhandClaude Fable 5.1
cb5771fa71
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Co-Authored-By: Claude Fable 5.1 <[email protected]> Claude-Session: https://claude.ai/code/session_01YJPeT6WA2e7YvAnS875AHL
492 lines
21 KiB
Rust
492 lines
21 KiB
Rust
//! The pressure step of the embedded-boundary PISO: the masked five-point
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//! problem and the projection, split into its solve and apply halves so
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//! the overset coupling (`overset/`) can iterate the solve across two
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//! meshes before applying the correction once.
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use super::EmbeddedPisoSolver;
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use crate::CfdResult;
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use crate::solvers::incompressible::ale::SideBoundary;
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use crate::solvers::incompressible::poisson::{
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MultigridParameters, PoissonProblem, PoissonSolverKind, solve_multigrid_pcg_cached,
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};
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use crate::solvers::incompressible::{EmbeddedMask, FlowField};
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impl EmbeddedPisoSolver {
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/// The pressure-correction system of one projection as a
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/// [`PoissonProblem`]: active = fluid cells, coefficient `dt A / delta`
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/// across every fluid interior face and zero across every prescribed
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/// one (domain Velocity / SlipWall sides, non-fluid interior faces),
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/// the outlet's Dirichlet `p' = 0` half a cell away as a diagonal-only
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/// `extra_diag`, right-hand side the mass imbalance `sp`. Arm for arm
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/// the coefficients the SOR loop of [`Self::project`] forms in place.
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pub(super) fn poisson_problem(&self, field: &FlowField, dt: f64) -> PoissonProblem {
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let (nx, ny, dx, dy) = field.grid_info();
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let b = self.parameters.boundaries;
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let outlet = SideBoundary::PressureOutlet;
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let ae_interior = dt * dy / dx;
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let an_interior = dt * dx / dy;
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let ae_outlet = dt * dy / (0.5 * dx);
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let an_outlet = dt * dx / (0.5 * dy);
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let mut problem = PoissonProblem::new(nx, ny);
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for j in 0..ny {
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for i in 0..nx {
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let idx = j * nx + i;
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if !self.cell_is_fluid(j, i) {
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problem.active[idx] = false;
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continue;
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}
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let mut extra = 0.0;
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// An overset fringe neighbour is a Dirichlet cell: its
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// coefficient moves to the diagonal and its known p' to
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// the right-hand side (the outlet's construction).
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let mut rhs_extra = 0.0;
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if i + 1 == nx {
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if b.right == outlet {
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extra += ae_outlet;
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}
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} else if self.u_is_fluid(j, i + 1) {
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if self.is_fringe(j, i + 1) {
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extra += ae_interior;
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rhs_extra += ae_interior * self.fringe_correction(j, i + 1);
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} else {
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problem.ae[idx] = ae_interior;
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}
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}
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if i == 0 {
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if b.left == outlet {
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extra += ae_outlet;
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}
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} else if self.u_is_fluid(j, i) {
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if self.is_fringe(j, i - 1) {
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extra += ae_interior;
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rhs_extra += ae_interior * self.fringe_correction(j, i - 1);
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} else {
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problem.aw[idx] = ae_interior;
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}
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}
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if j + 1 == ny {
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if b.top == outlet {
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extra += an_outlet;
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}
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} else if self.v_is_fluid(j + 1, i) {
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if self.is_fringe(j + 1, i) {
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extra += an_interior;
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rhs_extra += an_interior * self.fringe_correction(j + 1, i);
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} else {
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problem.an[idx] = an_interior;
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}
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}
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if j == 0 {
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if b.bottom == outlet {
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extra += an_outlet;
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}
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} else if self.v_is_fluid(j, i) {
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if self.is_fringe(j - 1, i) {
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extra += an_interior;
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rhs_extra += an_interior * self.fringe_correction(j - 1, i);
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} else {
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problem.as_[idx] = an_interior;
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}
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}
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problem.extra_diag[idx] = extra;
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problem.rhs[idx] = field.sp[(j, i)] + rhs_extra;
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}
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}
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problem
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}
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/// One projection on the fluid cells: the fixed-grid PISO's, with a
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/// zero coefficient across every prescribed face (domain Velocity /
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/// SlipWall sides and every non-fluid interior face), a Dirichlet `p' =
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/// 0` half a cell beyond an outlet face, and the anchor on the first
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/// fluid cell when no outlet exists. Returns the normalised mass
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/// imbalance of the corrected field over the fluid cells.
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#[allow(clippy::too_many_lines)]
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/// One projection on the fluid cells: [`Self::solve_correction`] then
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/// [`Self::apply_correction`] — the two halves the overset coupling
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/// calls separately (several solves, one application).
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pub(super) fn project(
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&self,
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field: &mut FlowField,
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dt: f64,
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warm_start: bool,
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) -> CfdResult<f64> {
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self.solve_correction(field, dt, warm_start)?;
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Ok(self.apply_correction(field, dt))
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}
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/// The solve half of a projection: the continuity source from `u*`
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/// into `field.sp`, then `p'` into `field.p_prime` (multigrid PCG with
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/// the SOR fallback). Nothing else in `field` is touched.
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#[allow(clippy::too_many_lines)]
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pub(crate) fn solve_correction(
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&self,
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field: &mut FlowField,
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dt: f64,
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warm_start: bool,
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) -> CfdResult<()> {
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let (nx, ny, dx, dy) = field.grid_info();
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let rho = self.config.density;
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let b = self.parameters.boundaries;
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let outlet = SideBoundary::PressureOutlet;
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let any_outlet = [b.left, b.right, b.bottom, b.top].contains(&outlet);
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let anchor = self.mask.as_ref().map_or((1, 1), EmbeddedMask::anchor);
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// With `warm_start` (the FIRST corrector only), the previous
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// step's correction is the multigrid initial guess — the
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// correction field is temporally correlated step to step
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// (measured 2026-08-30 on the FSI2 rigid phase: 2.96 PCG
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// iterations/solve from zero, 1.27 warm). Later correctors
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// solve for a much SMALLER correction, and the first
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// corrector's p' is a WORSE guess than zero there (measured:
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// the all-correctors draft cost 3.9 iters/solve in the coupled
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// phase). The SOR fallback below still starts from zero,
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// exactly as before.
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let mut source_scale = 0.0;
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for j in 0..ny {
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for i in 0..nx {
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if !self.cell_is_fluid(j, i) {
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field.sp[(j, i)] = 0.0;
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continue;
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}
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let divergence_flux = rho
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* ((field.u_star[(j, i + 1)] - field.u_star[(j, i)]) * dy
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+ (field.v_star[(j + 1, i)] - field.v_star[(j, i)]) * dx);
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field.sp[(j, i)] = -divergence_flux;
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source_scale += divergence_flux.abs();
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}
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}
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// Swept-volume source (knob; see `swept_volume`): the corrected
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// field must satisfy Σ u·n A = −dV_f/dt in every interface cell.
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if let (true, Some(a_new), Some(a_old)) =
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(self.swept_volume != 0.0, &self.alpha_new, &self.alpha_old)
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{
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for j in 0..ny {
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for i in 0..nx {
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if !self.cell_is_fluid(j, i) {
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continue;
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}
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let k = j * nx + i;
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let da = a_new[k] - a_old[k];
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if da != 0.0 {
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field.sp[(j, i)] -= self.swept_volume * rho * da * dx * dy / dt;
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}
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}
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}
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}
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// Reporting-only divergence trace (RTX_EMBEDDED_TRACE_SP): where the
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// projection's source sits relative to the step's fresh cells, in
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// units of one whole cell volume per step (rho dx dy / dt).
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if warm_start && !self.fresh_trace.is_empty() {
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let unit = rho * dx * dy / dt;
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let is_fresh =
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|j: usize, i: usize| self.fresh_trace.iter().any(|&(a, b)| a == j && b == i);
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let is_nbr = |j: usize, i: usize| {
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self.fresh_trace.iter().any(|&(a, b)| {
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(a == j && (b + 1 == i || i + 1 == b)) || (b == i && (a + 1 == j || j + 1 == a))
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})
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};
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let (mut mf, mut mn, mut mo) = (0.0f64, 0.0f64, 0.0f64);
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let (mut arg, mut argv) = ((0usize, 0usize), 0.0f64);
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let mut sum_fresh = 0.0f64;
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for j in 0..ny {
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for i in 0..nx {
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if !self.cell_is_fluid(j, i) {
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continue;
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}
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let v = field.sp[(j, i)] / unit;
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if is_fresh(j, i) {
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mf = mf.max(v.abs());
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sum_fresh += v;
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} else if is_nbr(j, i) {
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mn = mn.max(v.abs());
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} else {
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mo = mo.max(v.abs());
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}
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if v.abs() > argv.abs() {
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argv = v;
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arg = (j, i);
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}
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}
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}
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let class = if is_fresh(arg.0, arg.1) {
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"FRESH"
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} else if is_nbr(arg.0, arg.1) {
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"NEIGHBOUR"
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} else {
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"other"
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};
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// The argmax cell's 3x3 neighbourhood: F = fluid, S = solid,
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// * = fresh this step (row above first).
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let mut hood = String::new();
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for dj in [1i64, 0, -1] {
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for di in [-1i64, 0, 1] {
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let (jj, ii) = (arg.0 as i64 + dj, arg.1 as i64 + di);
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let c = if jj < 0 || ii < 0 || jj >= ny as i64 || ii >= nx as i64 {
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'#'
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} else if is_fresh(jj as usize, ii as usize) {
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'*'
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} else if self.cell_is_fluid(jj as usize, ii as usize) {
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'F'
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} else {
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'S'
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};
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hood.push(c);
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}
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hood.push('/');
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}
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let fj = self.fresh_trace.iter().map(|c| c.0);
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let fi = self.fresh_trace.iter().map(|c| c.1);
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println!(
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" SP-TRACE fresh rows {:?}..{:?} cols {:?}..{:?}; argmax hood {hood}",
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fj.clone().min(),
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fj.max(),
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fi.clone().min(),
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fi.max()
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);
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println!(
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" SP-TRACE t = {:.6}: {} fresh cells; max |sp| {:+.3} cell-volumes/step at ({}, {}) [{class}]; \
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max over fresh {:.3}, neighbours {:.3}, others {:.3}; sum over fresh {:+.3}",
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self.time + dt,
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self.fresh_trace.len(),
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argv,
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arg.0,
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arg.1,
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mf,
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mn,
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mo,
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sum_fresh
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);
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}
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let ae_interior = dt * dy / dx;
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let an_interior = dt * dx / dy;
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// Outlet face: p' = 0 half a cell away.
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let ae_outlet = dt * dy / (0.5 * dx);
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let an_outlet = dt * dx / (0.5 * dy);
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let reference_flux = rho * self.config.reference_velocity * self.config.reference_length;
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let inner_stop = (self.inner_stop_factor * source_scale)
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.max(0.1 * self.parameters.tolerance * reference_flux)
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+ 1e-14;
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let mut multigrid_converged = false;
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if self.parameters.poisson_solver == PoissonSolverKind::Multigrid {
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// The same system the SOR loop below sweeps, handed to the
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// multigrid-preconditioned CG solver: anchored on the first
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// fluid cell when there is no outlet (the SOR loop pins it to
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// zero), level-free otherwise. Non-fluid cells and isolated
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// fluid cells are never written and keep `p' = 0`.
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let problem = self.poisson_problem(field, dt);
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// Warm start from the previous correction on the CURRENT
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// fluid cells; everything else stays zero, preserving the
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// p' = 0 invariant on non-fluid cells through the copy-back.
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let mut p_prime = vec![0.0; nx * ny];
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if warm_start {
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for j in 0..ny {
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for i in 0..nx {
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if self.cell_is_fluid(j, i) {
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p_prime[j * nx + i] = field.p_prime[(j, i)];
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}
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}
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}
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}
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let anchor_cell =
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(!any_outlet && !self.has_fringe()).then_some(anchor.0 * nx + anchor.1);
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let solution = solve_multigrid_pcg_cached(
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&problem,
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&mut p_prime,
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&MultigridParameters {
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precision: self.parameters.poisson_precision,
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smoother: self.parameters.poisson_smoother,
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..MultigridParameters::default()
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},
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inner_stop,
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anchor_cell,
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&mut self.pcg_cache.borrow_mut(),
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);
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let (s0, i0, c0, k0) = self.poisson_profile.get();
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self.poisson_profile.set((
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s0 + solution.setup_ns,
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i0 + solution.iterate_ns,
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c0 + 1,
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k0 + solution.iterations as u64,
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));
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// Unconverged: fall back to the SOR sweeps for this projection
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// rather than apply a correction that did not reach the stop.
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multigrid_converged = solution.converged;
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if multigrid_converged {
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for j in 0..ny {
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for i in 0..nx {
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field.p_prime[(j, i)] = p_prime[j * nx + i];
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}
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}
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self.stamp_fringe_correction(&mut field.p_prime);
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}
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}
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if !multigrid_converged {
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// The fallback is unchanged: SOR from zero, as it always ran.
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field.p_prime.fill(0.0);
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self.stamp_fringe_correction(&mut field.p_prime);
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let omega = 2.0 / (1.0 + (std::f64::consts::PI / nx.max(ny) as f64).sin());
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for _sweep in 0..2000 {
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let mut residual = 0.0;
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for j in 0..ny {
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for i in 0..nx {
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if !self.cell_is_fluid(j, i) {
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continue;
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}
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if !any_outlet && !self.has_fringe() && (j, i) == anchor {
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field.p_prime[(j, i)] = 0.0;
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continue;
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}
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// A coefficient is zero exactly when the face is
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// prescribed: a domain side with velocity data, or a
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// non-fluid interior face.
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let ae = if i + 1 == nx {
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if b.right == outlet { ae_outlet } else { 0.0 }
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} else if self.u_is_fluid(j, i + 1) {
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ae_interior
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} else {
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0.0
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};
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let aw = if i == 0 {
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if b.left == outlet { ae_outlet } else { 0.0 }
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} else if self.u_is_fluid(j, i) {
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ae_interior
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} else {
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0.0
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};
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let an = if j + 1 == ny {
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if b.top == outlet { an_outlet } else { 0.0 }
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} else if self.v_is_fluid(j + 1, i) {
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an_interior
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} else {
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0.0
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};
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let as_ = if j == 0 {
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if b.bottom == outlet { an_outlet } else { 0.0 }
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} else if self.v_is_fluid(j, i) {
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an_interior
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} else {
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0.0
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};
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let ap = ae + aw + an + as_;
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if ap == 0.0 {
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// An isolated fluid cell enclosed by prescribed
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// faces has no equation; leave p' = 0 there.
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continue;
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}
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let east = if i + 1 < nx {
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ae * field.p_prime[(j, i + 1)]
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} else {
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0.0
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};
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let west = if i > 0 {
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aw * field.p_prime[(j, i - 1)]
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} else {
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0.0
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};
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let north = if j + 1 < ny {
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an * field.p_prime[(j + 1, i)]
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} else {
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0.0
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};
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let south = if j > 0 {
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as_ * field.p_prime[(j - 1, i)]
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} else {
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0.0
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};
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let rhs = field.sp[(j, i)] + east + west + north + south;
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let p_old = field.p_prime[(j, i)];
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residual += (rhs - ap * p_old).abs();
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field.p_prime[(j, i)] = (1.0 - omega) * p_old + omega * rhs / ap;
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}
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}
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if residual < inner_stop {
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break;
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}
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}
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}
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Ok(())
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}
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/// The apply half of a projection: correct the fluid faces from `u*`
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/// with the `p'` in `field.p_prime` (outlet faces against `p' = 0`
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/// outside), add `p'` to `p` on the fluid cells, and return the
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/// normalised mass imbalance of the corrected field.
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pub(crate) fn apply_correction(&self, field: &mut FlowField, dt: f64) -> f64 {
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let (nx, ny, dx, dy) = field.grid_info();
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let rho = self.config.density;
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let b = self.parameters.boundaries;
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let outlet = SideBoundary::PressureOutlet;
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let reference_flux = rho * self.config.reference_velocity * self.config.reference_length;
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// Correct exactly the faces the equations treated as correctable:
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// fluid interior faces, and outlet faces against p' = 0 outside.
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for j in 0..ny {
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for i in 1..nx {
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if self.u_is_fluid(j, i) {
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let dp_dx = (field.p_prime[(j, i)] - field.p_prime[(j, i - 1)]) / dx;
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field.u[(j, i)] = field.u_star[(j, i)] - (dt / rho) * dp_dx;
|
||
}
|
||
}
|
||
if b.left == outlet {
|
||
let dp_dx = (field.p_prime[(j, 0)] - 0.0) / (0.5 * dx);
|
||
field.u[(j, 0)] = field.u_star[(j, 0)] - (dt / rho) * dp_dx;
|
||
}
|
||
if b.right == outlet {
|
||
let dp_dx = (0.0 - field.p_prime[(j, nx - 1)]) / (0.5 * dx);
|
||
field.u[(j, nx)] = field.u_star[(j, nx)] - (dt / rho) * dp_dx;
|
||
}
|
||
}
|
||
for i in 0..nx {
|
||
for j in 1..ny {
|
||
if self.v_is_fluid(j, i) {
|
||
let dp_dy = (field.p_prime[(j, i)] - field.p_prime[(j - 1, i)]) / dy;
|
||
field.v[(j, i)] = field.v_star[(j, i)] - (dt / rho) * dp_dy;
|
||
}
|
||
}
|
||
if b.bottom == outlet {
|
||
let dp_dy = (field.p_prime[(0, i)] - 0.0) / (0.5 * dy);
|
||
field.v[(0, i)] = field.v_star[(0, i)] - (dt / rho) * dp_dy;
|
||
}
|
||
if b.top == outlet {
|
||
let dp_dy = (0.0 - field.p_prime[(ny - 1, i)]) / (0.5 * dy);
|
||
field.v[(ny, i)] = field.v_star[(ny, i)] - (dt / rho) * dp_dy;
|
||
}
|
||
}
|
||
|
||
for j in 0..ny {
|
||
for i in 0..nx {
|
||
if self.cell_is_fluid(j, i) {
|
||
field.p[(j, i)] += field.p_prime[(j, i)];
|
||
}
|
||
}
|
||
}
|
||
|
||
let mut mass_imbalance = 0.0;
|
||
for j in 0..ny {
|
||
for i in 0..nx {
|
||
if !self.cell_is_fluid(j, i) {
|
||
continue;
|
||
}
|
||
let divergence_flux = rho
|
||
* ((field.u[(j, i + 1)] - field.u[(j, i)]) * dy
|
||
+ (field.v[(j + 1, i)] - field.v[(j, i)]) * dx);
|
||
mass_imbalance += divergence_flux.abs();
|
||
}
|
||
}
|
||
|
||
if reference_flux > 0.0 {
|
||
mass_imbalance / reference_flux
|
||
} else {
|
||
mass_imbalance
|
||
}
|
||
}
|
||
}
|