embedded3 S2-8 instrument: the load routes in PARTS per body — exchange split into diffusive / convective (cut_wall_exchange_parts), a diagnostic x window on every load route (exchange::set_load_window), the flag test as a 2D periodic slab (RTX_E3_FLAG_NZ) with an amplitude knob (RTX_E3_FLAG_AMP, 0 = frozen) and a PARTS summary; cut_wall_force / _per_span moved to exchange.rs (cutwall.rs line cap)

Co-Authored-By: Claude Fable 5.1 <[email protected]>

crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/cutwall.rs

@@ -16,6 +16,7 @@
 use super::Grid;
 use super::body::Body;
 use super::cut::CutGeometry;
+use super::exchange::in_load_window;
 use super::field::Field;
 use super::step::{Boundaries, Side};
 use super::wall::{FaceKind, Mask};
@@ -589,37 +590,6 @@ impl Mask {
         flux
     }
 
-    /// The cut-cell load route: the force on the body from the operators
-    /// themselves — `Σ_c p_c W_c` over the cells plus the implicit wall
-    /// shear `Σ_f μ A_w (u_f − U_b)/d_f` over the unknown faces. `None`
-    /// without a cut geometry.
-    pub fn cut_wall_force(&self, body: &Body, f: &Field, mu: f64, t: f64) -> Option<[f64; 3]> {
-        let (p, s) = self.cut_wall_force_parts(body, f, mu, t)?;
-        let x = self.cut_wall_exchange_force(body, f, mu, self.density, t, None)?;
-        Some([p[0] + s[0] + x[0], p[1] + s[1] + x[1], p[2] + s[2] + x[2]])
-    }
-
-    /// The cut-cell load route restricted to the cells (and faces) of the
-    /// planes `k0..k1`, divided by the slab's thickness: the load per unit
-    /// span on a body's mid-section.
-    pub fn cut_wall_force_per_span(
-        &self,
-        body: &Body,
-        f: &Field,
-        mu: f64,
-        t: f64,
-        (k0, k1): (usize, usize),
-    ) -> Option<[f64; 3]> {
-        let (p, s) = self.cut_wall_force_parts_in(body, f, mu, t, Some((k0, k1)))?;
-        let x = self.cut_wall_exchange_force(body, f, mu, self.density, t, Some((k0, k1)))?;
-        let lz = (k1 - k0) as f64 * self.grid.dz;
-        Some([
-            (p[0] + s[0] + x[0]) / lz,
-            (p[1] + s[1] + x[1]) / lz,
-            (p[2] + s[2] + x[2]) / lz,
-        ])
-    }
-
     /// The cut-cell load route split into its pressure and shear parts.
     pub fn cut_wall_force_parts(
         &self,
@@ -631,7 +601,7 @@ impl Mask {
         self.cut_wall_force_parts_in(body, f, mu, t, None)
     }
 
-    fn cut_wall_force_parts_in(
+    pub(super) fn cut_wall_force_parts_in(
         &self,
         body: &Body,
         f: &Field,
@@ -646,8 +616,9 @@ impl Mask {
         let mut pressure = [0.0; 3];
         let mut force = [0.0; 3];
         for (idx, w) in cut.wall.iter().enumerate() {
-            let k = g.kji(idx).0;
-            if self.cell_fluid[idx] && k >= k0 && k < k1 {
+            let (k, _, i) = g.kji(idx);
+            if self.cell_fluid[idx] && k >= k0 && k < k1 && in_load_window((i as f64 + 0.5) * g.dx)
+            {
                 for c in 0..3 {
                     pressure[c] += f.p[idx] * w[c];
                 }
@@ -676,7 +647,7 @@ impl Mask {
                             1 => self.v_kind[idx],
                             _ => self.w_kind[idx],
                         };
-                        if kind != FaceKind::Fluid {
+                        if kind != FaceKind::Fluid || !in_load_window(lat.face_position(c, p)[0]) {
                             continue;
                         }
                         let cv = self.cv_geometry(c, p);

crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/exchange.rs

@@ -13,7 +13,55 @@ use super::field::Field;
 use super::wall::{FaceKind, Mask};
 use crate::solvers::incompressible::ConvectionScheme;
 
+/// DIAGNOSTIC: an x window on every load route (`set_load_window`): cells and
+/// faces outside `[x0, x1)` are skipped — the cylinder and the flag read
+/// apart. Process-wide; `None` (the default) reads the whole body.
+static LOAD_WINDOW: std::sync::Mutex<Option<(f64, f64)>> = std::sync::Mutex::new(None);
+
+/// Set or clear the diagnostic x window of the load routes.
+pub fn set_load_window(window: Option<(f64, f64)>) {
+    *LOAD_WINDOW.lock().expect("load window") = window;
+}
+
+pub(super) fn in_load_window(x: f64) -> bool {
+    LOAD_WINDOW
+        .lock()
+        .expect("load window")
+        .is_none_or(|(x0, x1)| x >= x0 && x < x1)
+}
+
 impl Mask {
+    /// The cut-cell load route: the force on the body from the operators
+    /// themselves — `Σ_c p_c W_c` over the cells plus the implicit wall
+    /// shear `Σ_f μ A_w (u_f − U_b)/d_f` over the unknown faces. `None`
+    /// without a cut geometry.
+    pub fn cut_wall_force(&self, body: &Body, f: &Field, mu: f64, t: f64) -> Option<[f64; 3]> {
+        let (p, s) = self.cut_wall_force_parts(body, f, mu, t)?;
+        let x = self.cut_wall_exchange_force(body, f, mu, self.density, t, None)?;
+        Some([p[0] + s[0] + x[0], p[1] + s[1] + x[1], p[2] + s[2] + x[2]])
+    }
+
+    /// The cut-cell load route restricted to the cells (and faces) of the
+    /// planes `k0..k1`, divided by the slab's thickness: the load per unit
+    /// span on a body's mid-section.
+    pub fn cut_wall_force_per_span(
+        &self,
+        body: &Body,
+        f: &Field,
+        mu: f64,
+        t: f64,
+        (k0, k1): (usize, usize),
+    ) -> Option<[f64; 3]> {
+        let (p, s) = self.cut_wall_force_parts_in(body, f, mu, t, Some((k0, k1)))?;
+        let x = self.cut_wall_exchange_force(body, f, mu, self.density, t, Some((k0, k1)))?;
+        let lz = (k1 - k0) as f64 * self.grid.dz;
+        Some([
+            (p[0] + s[0] + x[0]) / lz,
+            (p[1] + s[1] + x[1]) / lz,
+            (p[2] + s[2] + x[2]) / lz,
+        ])
+    }
+
     /// The momentum the fluid's face control volumes exchange with the
     /// prescribed faces beside them, as a force on the body (the negative
     /// of the force on the fluid), over the z planes `planes` (all when
@@ -27,6 +75,23 @@ impl Mask {
         t: f64,
         planes: Option<(usize, usize)>,
     ) -> Option<[f64; 3]> {
+        let (d, c) = self.cut_wall_exchange_parts(body, f, mu, rho, t, planes)?;
+        Some([d[0] + c[0], d[1] + c[1], d[2] + c[2]])
+    }
+
+    /// The exchange split into its DIFFUSIVE and CONVECTIVE parts (forces on
+    /// the body). On a wall at rest the convective part is the scheme's
+    /// flux correction only; on a moving wall it carries `ρ m (u_face − u_f)`
+    /// with `m` the wall's own swept flux — O(v_wall h / ν) times the shear.
+    pub fn cut_wall_exchange_parts(
+        &self,
+        body: &Body,
+        f: &Field,
+        mu: f64,
+        rho: f64,
+        t: f64,
+        planes: Option<(usize, usize)>,
+    ) -> Option<([f64; 3], [f64; 3])> {
         let _ = body;
         let _ = t;
         self.cut.as_ref()?;
@@ -55,6 +120,7 @@ impl Mask {
             |a: [i64; 3], b: [i64; 3], s: i64| [a[0] + s * b[0], a[1] + s * b[1], a[2] + s * b[2]];
         let upwind = |m: f64, up: f64, dn: f64| if m >= 0.0 { up } else { dn };
         let mut force = [0.0; 3];
+        let mut convective = [0.0; 3];
         for c in 0..3 {
             let (ir, jr, kr) = match c {
                 0 => (1..nx, 0..ny, k0..k1),
@@ -67,7 +133,9 @@ impl Mask {
                     for i in ir.clone() {
                         let p = [i as i64, j as i64, k as i64];
                         let idx = lat.face(c, p).expect("face");
-                        if kind(c, idx) != FaceKind::Fluid {
+                        if kind(c, idx) != FaceKind::Fluid
+                            || !in_load_window(lat.face_position(c, p)[0])
+                        {
                             continue;
                         }
                         let cv = self.cv_geometry(c, p);
@@ -123,9 +191,9 @@ impl Mask {
                                         scheme.face_correction(up2, un, u0)
                                     };
                                     let u_face = upwind(m_plus, u0, un) + delta;
-                                    let on_fluid = -rho * m_plus * (u_face - u0)
-                                        + mu * cv.ap[d][1] * a_d * (un - u0) / solid_spacing(1.0);
-                                    force[c] -= on_fluid;
+                                    convective[c] -= -rho * m_plus * (u_face - u0);
+                                    force[c] -=
+                                        mu * cv.ap[d][1] * a_d * (un - u0) / solid_spacing(1.0);
                                 }
                             }
                             // Minus side.
@@ -140,9 +208,9 @@ impl Mask {
                                         scheme.face_correction(up1, u0, ud)
                                     };
                                     let u_face = upwind(m_minus, ud, u0) + delta;
-                                    let on_fluid = rho * m_minus * (u_face - u0)
-                                        + mu * cv.ap[d][0] * a_d * (ud - u0) / solid_spacing(-1.0);
-                                    force[c] -= on_fluid;
+                                    convective[c] -= rho * m_minus * (u_face - u0);
+                                    force[c] -=
+                                        mu * cv.ap[d][0] * a_d * (ud - u0) / solid_spacing(-1.0);
                                 }
                             }
                         }
@@ -150,7 +218,7 @@ impl Mask {
                 }
             }
         }
-        Some(force)
+        Some((force, convective))
     }
 
     /// The closure lag of a moving body's pressure correction: the

crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/reconstruct.rs

@@ -52,7 +52,7 @@ impl Mask {
                 continue;
             }
             let (k, j, i) = g.kji(idx);
-            if k < k0 || k >= k1 {
+            if k < k0 || k >= k1 || !super::exchange::in_load_window((i as f64 + 0.5) * g.dx) {
                 continue;
             }
             let xc = [

crates/specialized/rtx-cfd/tests/embedded3_flag_wake.rs

@@ -65,12 +65,19 @@ fn mode(s: f64) -> f64 {
 /// Centreline deflection and its velocity at arc parameter `s`, time `t`.
 fn deflection(s: f64, t: f64) -> (f64, f64) {
     let w = 2.0 * std::f64::consts::PI * FREQ;
+    let amp = amplitude();
     (
-        AMP * mode(s) * (w * t).sin(),
-        AMP * mode(s) * w * (w * t).cos(),
+        amp * mode(s) * (w * t).sin(),
+        amp * mode(s) * w * (w * t).cos(),
     )
 }
 
+/// The tip amplitude: `RTX_E3_FLAG_AMP` (default 0.084; 0 freezes the flag —
+/// the static control of the load routes).
+fn amplitude() -> f64 {
+    env_f("RTX_E3_FLAG_AMP", AMP)
+}
+
 /// Signed distance to the deflected flag's cross-section (a capsule
 /// around the centreline polyline of `n` segments) and the centreline's
 /// transverse velocity at the closest point.
@@ -131,7 +138,10 @@ fn flag_wake_on_the_device() {
     let periods = env_f("RTX_E3_FLAG_PERIODS", 2.0);
     let h = H / ny as f64;
     let nx = (L / h).round() as usize;
-    let nz = ny;
+    // `RTX_E3_FLAG_NZ=4`: a thin slab periodic in z with the 2D inflow (Ū = 1) — the
+    // flag as a 2D problem, minutes per rung: the instrument for the load routes' parts.
+    let slab_nz = env_f("RTX_E3_FLAG_NZ", 0.0) as usize;
+    let nz = if slab_nz > 0 { slab_nz } else { ny };
     let r_edge = h;
     let dt_cfl = 0.3 * h / (U_M.max(2.0 * std::f64::consts::PI * FREQ * AMP));
     // `RTX_E3_FLAG_DT_SCALE` scales the step (the dt ladder of the loads).
@@ -155,18 +165,36 @@ fn flag_wake_on_the_device() {
             tolerance: 1e-8,
             convection_scheme: ConvectionScheme::TvdVanAlbada,
             wall_scheme: WallScheme::CutCell,
-            boundaries: Boundaries {
-                x1: Side::PressureOutlet,
-                ..Boundaries::default()
+            boundaries: if slab_nz > 0 {
+                Boundaries {
+                    x1: Side::PressureOutlet,
+                    z0: Side::Periodic,
+                    z1: Side::Periodic,
+                    ..Boundaries::default()
+                }
+            } else {
+                Boundaries {
+                    x1: Side::PressureOutlet,
+                    ..Boundaries::default()
+                }
             },
             // The narrow band: the flag's tip speed bounds the surface motion.
-            max_surface_speed: Some(2.0 * std::f64::consts::PI * FREQ * AMP * 1.05),
+            max_surface_speed: Some(
+                (2.0 * std::f64::consts::PI * FREQ * amplitude() * 1.05).max(1e-3),
+            ),
             ..Parameters::default()
         },
     );
-    solver.set_boundary_velocity(|x, y, z, _t| {
+    let inflow_at = move |y: f64, z: f64| {
+        if slab_nz > 0 {
+            6.0 * y * (H - y) / (H * H)
+        } else {
+            inflow(y, z)
+        }
+    };
+    solver.set_boundary_velocity(move |x, y, z, _t| {
         if x <= 0.0 {
-            (inflow(y, z), 0.0, 0.0)
+            (inflow_at(y, z), 0.0, 0.0)
         } else {
             (0.0, 0.0, 0.0)
         }
@@ -186,7 +214,7 @@ fn flag_wake_on_the_device() {
     let mut field = Field::new(g);
     for k in 0..nz {
         for j in 0..ny {
-            let u0 = inflow((j as f64 + 0.5) * h, (k as f64 + 0.5) * h);
+            let u0 = inflow_at((j as f64 + 0.5) * h, (k as f64 + 0.5) * h);
             for i in 0..=nx {
                 field.u[g.uface(k, j, i)] = u0;
             }
@@ -217,9 +245,17 @@ fn flag_wake_on_the_device() {
     let last_period_start = t_end - period;
     let mut next_phase = 0;
     let mid = nz / 2;
-    let slab = (mid - 2, mid + 2);
+    let slab = if slab_nz > 0 {
+        (0, nz)
+    } else {
+        (mid - 2, mid + 2)
+    };
+    let width = nz as f64 * h;
     let start = std::time::Instant::now();
     let mut drag_rec_sum = 0.0;
+    // The routes' PARTS over the whole body (x, per unit width): operator
+    // pressure / shear / exchange, reconstructed pressure / shear.
+    let mut parts = [[0.0_f64; 6]; 3];
     let (mut drag_sum, mut lift_min, mut lift_max, mut samples) =
         (0.0, f64::INFINITY, f64::NEG_INFINITY, 0usize);
     let mut worst_residual = 0.0_f64;
@@ -283,6 +319,30 @@ fn flag_wake_on_the_device() {
                     .unwrap();
                 }
                 if t >= last_period_start {
+                    use rtx_cfd::solvers::incompressible::embedded3::exchange::set_load_window;
+                    // whole body, the cylinder (x < 0.252), the flag
+                    for (w, window) in [None, Some((0.0, 0.252)), Some((0.252, 10.0))]
+                        .into_iter()
+                        .enumerate()
+                    {
+                        set_load_window(window);
+                        let (po, so) = mask
+                            .cut_wall_force_parts(body, &field, RHO * NU, t)
+                            .expect("parts");
+                        let (xd, xc) = mask
+                            .cut_wall_exchange_parts(body, &field, RHO * NU, RHO, t, None)
+                            .expect("exchange");
+                        let (pr, sr) = mask
+                            .cut_wall_force_reconstructed_parts(body, &field, RHO * NU, t, None)
+                            .expect("reconstructed parts");
+                        for (acc, v) in parts[w]
+                            .iter_mut()
+                            .zip([po[0], so[0], xd[0], xc[0], pr[0], sr[0]])
+                        {
+                            *acc += v / width;
+                        }
+                    }
+                    set_load_window(None);
                     drag_sum += fs[0];
                     drag_rec_sum += fr[0];
                     lift_min = lift_min.min(fs[1]);
@@ -306,6 +366,21 @@ fn flag_wake_on_the_device() {
         next_phase,
         start.elapsed().as_secs_f64()
     );
+    let n = samples.max(1) as f64;
+    for (name, q) in ["whole body", "cylinder", "flag"].iter().zip(parts) {
+        println!(
+            "  PARTS ny {ny} amp {:.3} {name} (x, N/m of width): operator pressure {:.2} + shear {:.2} + exchange diffusive {:.2} + convective {:.2} = {:.2}; reconstructed pressure {:.2} + shear {:.2} = {:.2}",
+            amplitude(),
+            q[0] / n,
+            q[1] / n,
+            q[2] / n,
+            q[3] / n,
+            (q[0] + q[1] + q[2] + q[3]) / n,
+            q[4] / n,
+            q[5] / n,
+            (q[4] + q[5]) / n
+        );
+    }
     if let Some(t) = device.timers() {
         println!("  timers: {t:?}");
     }