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tests/test_pipe.py

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+# tests/test_pipe.py
+import numpy as np
+import pytest
+from pipe import Pipe
+
+
+GAMMA = 1.4
+R_GAS = 287.0
+
+
+def test_pipe_uniform_initialization_all_cells_identical():
+    """
+    Initial state: uniform P, T, u=0 across all N cells.
+    All cells should have identical W. primitives() should round-trip
+    back to u=0 and P=P_init.
+    """
+    pipe = Pipe(L=1.0, D=5e-3, N=20,
+                P_init=1e5, T_init=300.0,
+                gamma=GAMMA, R_gas=R_GAS)
+
+    # All cells identical
+    for i in range(1, pipe.N):
+        assert np.allclose(pipe.W[:, i], pipe.W[:, 0], rtol=1e-14)
+
+    rho, u, P, a = pipe.primitives()
+    rho_expected = 1e5 / (R_GAS * 300.0)
+    assert np.allclose(u, 0.0)
+    assert np.allclose(P, 1e5, rtol=1e-10)
+    assert np.allclose(rho, rho_expected, rtol=1e-10)
+
+    # Sound speed a = sqrt(gamma * P / rho)
+    a_expected = np.sqrt(GAMMA * 1e5 / rho_expected)
+    assert np.allclose(a, a_expected, rtol=1e-10)
+
+    # Geometric sanity
+    assert pipe.dx == 1.0 / 20
+    assert pipe.x_centers.shape == (20,)
+    assert abs(pipe.x_centers[0] - 0.025) < 1e-14
+    assert abs(pipe.x_centers[-1] - 0.975) < 1e-14
+
+
+def test_pipe_uniform_state_plus_matching_boundary_flux_is_static():
+    """
+    If all cells have identical W (so all internal HLL fluxes are
+    identical to the physical flux F(W) = [0, P, 0] for u=0 state),
+    and we pass in boundary fluxes equal to [0, P, 0] as well, then
+    every difference (flux[i+1] - flux[i]) is zero, so W must not
+    change after one step. Verify to machine precision.
+    """
+    pipe = Pipe(L=1.0, D=5e-3, N=20,
+                P_init=1e5, T_init=300.0,
+                gamma=GAMMA, R_gas=R_GAS)
+
+    W_before = pipe.W.copy()
+    # Boundary flux matching the static interior: [rho*u, rho*u^2+P, u*(E+P)]
+    # with u=0 -> [0, P, 0]
+    flux_boundary = np.array([0.0, 1e5, 0.0])
+    pipe.step(flux_boundary, flux_boundary, dt=1e-5)
+    assert np.allclose(pipe.W, W_before, atol=1e-6, rtol=1e-12)