rtx-cfd: OverlapMap::region_force — momentum flux into a background region (control-volume face formula, one-sided next to holes); overset_cfd1 prints the four momentum routes (CV box, ring outer, hole boundary, wall) and their defects at the settled state

Co-Authored-By: Claude Fable 5.1 <[email protected]>
Claude-Session: https://claude.ai/code/session_01X2GmJXeQ2njUecEKiJZ1G2

crates/specialized/rtx-cfd/src/solvers/incompressible/overset/overlap.rs

@@ -509,6 +509,160 @@ impl OverlapMap {
 
     /// Background-side overlap mass defect: `Σ_fringe |Σ_f sign F_f|`
     /// (volume flux), the continuity the fringe cells do not enforce.
+    /// The force the background transmits INTO the region of cells whose
+    /// class satisfies `inside` — the sum over the region's boundary faces
+    /// of `sigma·n − rho u (u·n)` with `n` pointing out of the region, the
+    /// control-volume formula of `EmbeddedMask::control_volume_force`
+    /// without the unsteady term (a settled-state diagnostic). Values are
+    /// taken from non-hole cells only: a face next to a hole cell uses the
+    /// one-sided stencil from its valid side, so the hole boundary itself
+    /// (`inside = Hole`) is evaluated from the fringe's stamped values.
+    ///
+    /// Two regions make the P4 momentum-defect measurement: `Fringe |
+    /// Hole` (what the active region passes to the ring) and `Hole` (what
+    /// the ring passes on); their difference is the fringe ring's momentum
+    /// defect, and the hole boundary against the patch's wall force is the
+    /// patch region's.
+    pub fn region_force(
+        &self,
+        field: &FlowField,
+        rho: f64,
+        mu: f64,
+        inside: impl Fn(CellClass) -> bool,
+    ) -> (f64, f64) {
+        let (nx, ny, dx, dy) = (self.nx, self.ny, self.dx, self.dy);
+        let valid = |j: isize, i: isize| -> bool {
+            j >= 0
+                && i >= 0
+                && (j as usize) < ny
+                && (i as usize) < nx
+                && self.class(j as usize, i as usize) != CellClass::Hole
+        };
+        let is_in = |j: isize, i: isize| -> bool {
+            j >= 0
+                && i >= 0
+                && (j as usize) < ny
+                && (i as usize) < nx
+                && inside(self.class(j as usize, i as usize))
+        };
+        // Face-located u is valid when either adjacent cell is; likewise v.
+        let uf_valid = |j: isize, i: isize| valid(j, i - 1) || valid(j, i);
+        let vf_valid = |j: isize, i: isize| valid(j - 1, i) || valid(j, i);
+        let u = |j: isize, i: isize| field.u[(j as usize, i as usize)];
+        let v = |j: isize, i: isize| field.v[(j as usize, i as usize)];
+        let p = |j: isize, i: isize| field.p[(j as usize, i as usize)];
+        // Cell-centred v and u (averages of the cell's two faces).
+        let v_c = |j: isize, i: isize| 0.5 * (v(j, i) + v(j + 1, i));
+        let u_c = |j: isize, i: isize| 0.5 * (u(j, i) + u(j, i + 1));
+        // Average of the valid members of a pair, or `None`.
+        let pair = |a: Option<f64>, b: Option<f64>| match (a, b) {
+            (Some(a), Some(b)) => Some(0.5 * (a + b)),
+            (Some(a), None) | (None, Some(a)) => Some(a),
+            (None, None) => None,
+        };
+        // Derivative across `x0 → x1 → x2` (spacing `h`): central when both
+        // ends are valid, one-sided otherwise, zero when nothing is.
+        let deriv = |m: Option<f64>, c: f64, pl: Option<f64>, h: f64| match (m, pl) {
+            (Some(m), Some(pl)) => (pl - m) / (2.0 * h),
+            (Some(m), None) => (c - m) / h,
+            (None, Some(pl)) => (pl - c) / h,
+            (None, None) => 0.0,
+        };
+        let (mut fx, mut fy) = (0.0, 0.0);
+        for jc in 0..ny as isize {
+            for ic in 0..nx as isize {
+                if !is_in(jc, ic) {
+                    continue;
+                }
+                // Vertical faces: west (u face ic, n = −x) and east (ic + 1, +x).
+                for (i, sign, nj, ni) in [(ic, -1.0, jc, ic - 1), (ic + 1, 1.0, jc, ic + 1)] {
+                    if is_in(nj, ni) || nj < 0 || ni < 0 || ni >= nx as isize {
+                        continue;
+                    }
+                    let j = jc;
+                    let un = u(j, i);
+                    let p_f = pair(
+                        valid(j, i - 1).then(|| p(j, i - 1)),
+                        valid(j, i).then(|| p(j, i)),
+                    )
+                    .unwrap_or(0.0);
+                    let dudx = deriv(
+                        uf_valid(j, i - 1).then(|| u(j, i - 1)),
+                        un,
+                        (i < nx as isize && uf_valid(j, i + 1)).then(|| u(j, i + 1)),
+                        dx,
+                    );
+                    let dudy = deriv(
+                        (j >= 1 && uf_valid(j - 1, i)).then(|| u(j - 1, i)),
+                        un,
+                        (j + 1 < ny as isize && uf_valid(j + 1, i)).then(|| u(j + 1, i)),
+                        dy,
+                    );
+                    let vw = valid(j, i - 1).then(|| v_c(j, i - 1));
+                    let ve = valid(j, i).then(|| v_c(j, i));
+                    let dvdx = match (vw, ve) {
+                        (Some(a), Some(b)) => (b - a) / dx,
+                        (Some(a), None) => {
+                            (a - if valid(j, i - 2) { v_c(j, i - 2) } else { a }) / dx
+                        }
+                        (None, Some(b)) => {
+                            ((if valid(j, i + 1) { v_c(j, i + 1) } else { b }) - b) / dx
+                        }
+                        (None, None) => 0.0,
+                    };
+                    let v_f = pair(vw, ve).unwrap_or(0.0);
+                    let sxx = -p_f + 2.0 * mu * dudx;
+                    let sxy = mu * (dudy + dvdx);
+                    fx += sign * (sxx - rho * un * un) * dy;
+                    fy += sign * (sxy - rho * v_f * un) * dy;
+                }
+                // Horizontal faces: south (v face jc, n = −y) and north (jc + 1, +y).
+                for (j, sign, nj, ni) in [(jc, -1.0, jc - 1, ic), (jc + 1, 1.0, jc + 1, ic)] {
+                    if is_in(nj, ni) || nj < 0 || nj >= ny as isize {
+                        continue;
+                    }
+                    let i = ic;
+                    let vn = v(j, i);
+                    let p_f = pair(
+                        valid(j - 1, i).then(|| p(j - 1, i)),
+                        valid(j, i).then(|| p(j, i)),
+                    )
+                    .unwrap_or(0.0);
+                    let dvdy = deriv(
+                        vf_valid(j - 1, i).then(|| v(j - 1, i)),
+                        vn,
+                        (j < ny as isize && vf_valid(j + 1, i)).then(|| v(j + 1, i)),
+                        dy,
+                    );
+                    let dvdx = deriv(
+                        (i >= 1 && vf_valid(j, i - 1)).then(|| v(j, i - 1)),
+                        vn,
+                        (i + 1 < nx as isize && vf_valid(j, i + 1)).then(|| v(j, i + 1)),
+                        dx,
+                    );
+                    let us = valid(j - 1, i).then(|| u_c(j - 1, i));
+                    let un_ = valid(j, i).then(|| u_c(j, i));
+                    let dudy = match (us, un_) {
+                        (Some(a), Some(b)) => (b - a) / dy,
+                        (Some(a), None) => {
+                            (a - if valid(j - 2, i) { u_c(j - 2, i) } else { a }) / dy
+                        }
+                        (None, Some(b)) => {
+                            ((if valid(j + 1, i) { u_c(j + 1, i) } else { b }) - b) / dy
+                        }
+                        (None, None) => 0.0,
+                    };
+                    let u_f = pair(us, un_).unwrap_or(0.0);
+                    let syy = -p_f + 2.0 * mu * dvdy;
+                    let sxy = mu * (dudy + dvdx);
+                    fx += sign * (sxy - rho * u_f * vn) * dx;
+                    fy += sign * (syy - rho * vn * vn) * dx;
+                }
+            }
+        }
+        (fx, fy)
+    }
+
     pub fn background_mass_defect(&self, field: &FlowField) -> f64 {
         let (dx, dy) = (self.dx, self.dy);
         self.fringe_cells