P6-b design 2: the Robin wall on the patch's Inner side — RobinWall { alpha, datum } with the wall velocity u_s + (t_f − datum)/α (explicit, damped by the wall's own viscous gain μ/(α d)) and the compliant-wall pressure term |S| p'/α implicit in the projection (the added-mass operator in the fluid's own response); Dirichlet bit for bit when off; MMS pin on the skewed annulus (orders 2.46/2.13 at α = 10 and 100 μ/h, the Dirichlet values; a 1e12 wall reproduces Dirichlet to 2e-6); OversetPisoSolver::patch_mut; harness knob RTX_FSI2O_ROBIN_ALPHA with the previous pass's tractions as the datum, printed in the header

Co-Authored-By: Claude Fable 5.1 <[email protected]>
Claude-Session: https://claude.ai/code/session_01YJPeT6WA2e7YvAnS875AHL

crates/specialized/rtx-cfd/src/solvers/incompressible/curvilinear/projection.rs

@@ -6,7 +6,7 @@
 use super::{CurvilinearPisoSolver, PatchField, PressureSystem, SideBc, StepGeometry};
 use crate::mesh::PatchSide;
 use crate::solvers::incompressible::sparse_bicgstab::{
-    BicgstabResult, CsrMatrix, bicgstab_jacobi, project_mean,
+    bicgstab_jacobi, project_mean, BicgstabResult, CsrMatrix,
 };
 
 impl CurvilinearPisoSolver {
@@ -116,7 +116,9 @@ impl CurvilinearPisoSolver {
         ]
         .iter()
         .any(|&s| self.params.boundaries.get(s) == SideBc::Outlet);
-        if has_outlet || self.acceptors.is_some() {
+        // A Robin wall absorbs the net flux through its compliance (the
+        // pressure system is then not pure Neumann).
+        if has_outlet || self.acceptors.is_some() || self.robin.is_some() {
             return 0.0;
         }
         let (mut net, mut total_len) = (0.0, 0.0);
@@ -158,6 +160,15 @@ impl CurvilinearPisoSolver {
                 continue;
             }
             for (f, sign) in mesh.cell_faces(c) {
+                if let Some(w) = &self.robin {
+                    if mesh.side(f) == Some(PatchSide::Inner) {
+                        // The compliant wall: outward flux `+|S| p'_c / alpha`.
+                        let sv = mesh.faces()[f].s;
+                        let len = (sv[0] * sv[0] + sv[1] * sv[1]).sqrt();
+                        tri.push((c, c, len / w.alpha));
+                        any_dirichlet = true;
+                    }
+                }
                 self.ops
                     .face_gradient_coeffs(mesh, &self.params.boundaries, f, &mut coefs);
                 if mesh.side(f).is_some() && !coefs.is_empty() {
@@ -257,6 +268,16 @@ impl CurvilinearPisoSolver {
         for f in 0..mesh.faces().len() {
             field.flux[f] -= dt / rho * lp[f];
         }
+        if let Some(w) = &self.robin {
+            // The compliant wall's flux answer: `δu_b = −p' S / (alpha |S|)`,
+            // `δF = δu_b · S = −p' |S| / alpha` in the face's own orientation.
+            for &f in &self.robin_faces {
+                let c = mesh.boundary_cell(f);
+                let sv = mesh.faces()[f].s;
+                let len = (sv[0] * sv[0] + sv[1] * sv[1]).sqrt();
+                field.flux[f] -= pc[c] * len / w.alpha;
+            }
+        }
         for c in 0..mesh.cell_count() {
             if self.is_acceptor(c) {
                 continue;