test: integrate explicitly repinned uniform LES shear diagnostic

tests/validation/les_flow_oracle.py

@@ -0,0 +1,56 @@
+"""Independent 1D continuum oracle; no LBM closure/header or GPU imports."""
+
+import numpy as np
+
+H, U, NU, DELTA = 32.0, 0.04, 0.02, 1.0
+TIMES = tuple(round(v * H**2 / (np.pi**2 * NU)) for v in (0.1, 0.2, 0.4))
+
+
+def solve(cs, n=256, times=TIMES, *, h=H, u0=U, nu=NU, delta=DELTA, cfl=0.4):
+    """FV centered face flux plus SSPRK2, zero Dirichlet at 0,h.
+
+    du/dt = d/dy[(nu + (cs*delta)^2*|du/dy|) du/dy].
+    The oracle refinement dx=h/n MUST NOT replace the LES filter delta.
+    """
+    if not np.isfinite(cfl) or not 0 < cfl <= 0.4:
+        raise ValueError("cfl must be finite and in (0, .4]")
+    dx = h / n
+    y = (np.arange(n) + 0.5) * dx
+    u = u0 * np.sin(np.pi * y / h)
+    a = (cs * delta) ** 2
+
+    def gradients(v):
+        g = np.empty(n + 1)
+        g[1:-1] = np.diff(v) / dx
+        g[0], g[-1] = 2 * v[0] / dx, -2 * v[-1] / dx
+        return g
+
+    def rhs(v):
+        g = gradients(v)
+        flux = (nu + a * np.abs(g)) * g
+        return np.diff(flux) / dx
+
+    t = 0.0
+    out = {}
+    for target in times:
+        if target < t:
+            raise ValueError("times must be nondecreasing and nonnegative")
+        while t < target:
+            # Nonlinear flux derivative is nu+2*a*abs(gradient).
+            dt = min(
+                target - t, cfl * dx * dx / (nu + 2 * a * np.max(np.abs(gradients(u))))
+            )
+            v = u + dt * rhs(u)
+            u = 0.5 * u + 0.5 * (v + dt * rhs(v))
+            t += dt
+        out[int(target)] = u.copy()
+    return y, out
+
+
+def amplitude(y, u, h=H):
+    s = np.sin(np.pi * y / h)
+    return float(np.dot(u, s) / np.dot(s, s))
+
+
+def relative(a, b):
+    return float(np.linalg.norm(a - b) / np.linalg.norm(b))