test: add POST-G shear initialization counterfactual

tests/validation/taylor_green/shear_postg.py

@@ -0,0 +1,34 @@
+"""First-gradient POST-G initialization counterfactual, not a qualification preset.
+
+PRE F = feq - tau*A; POST G = feq - (tau - 1)*A. This low-Mach,
+first-order Chapman-Enskog approximation is not an exact discrete eigenstate.
+The physical viscous-stress factor tau - 1/2 is not the raw POST-G factor.
+"""
+
+import numpy as np
+
+import shear_nested as nested
+import shear_wave as sw
+from oracle import CX, CY, W, U, centers
+
+REFINEMENTS = nested.REFINEMENTS
+CASES = ((100, 128, 1, "constant"), (100, 512, 1, "constant"),
+         (100, 128, 3, "projected_linear"))
+INITIALIZATION_ID = "postg_first_gradient_v1"
+INITIALIZATION = (
+    "physical FP64 POST G=feq-(tau-1)A at actual cell centers; "
+    "A=3*w*U*cos(theta)*(c.e)*(c.k_level); rho=1; first-gradient low-Mach CE"
+)
+
+
+def initial(shape, level, length, viscosity):
+    """Return physical FP64 G; production initialize owns shifted FP32 encoding."""
+    x, y = centers(shape, level)
+    k = sw.wavevector(length)
+    theta = k[0] * x + k[1] * y + sw.PHI
+    k_level = k * 2.0**-level
+    tau = 0.5 + 3 * viscosity * 2**level
+    ce = CX * sw.E[0] + CY * sw.E[1]
+    ck = CX * k_level[0] + CY * k_level[1]
+    correction = (3 * W * ce * ck)[:, None, None] * U * np.cos(theta)
+    return sw.initial(shape, level, length, viscosity) - (tau - 1) * correction