Compare force term against conditions from Schiller

lbmpy/forcemodels.py

@@ -175,7 +175,7 @@ class Schiller:
         omega = get_shear_relaxation_rate(lb_method)
         omega_bulk = get_bulk_relaxation_rate(lb_method)
         G = (u * force.transpose() + force * u.transpose() - uf * sp.Rational(2, lb_method.dim)) * sp.Rational(1, 2) * \
-            (2 + omega) + uf * sp.Rational(1, 3) * (2 + omega_bulk)
+            (2 + omega) + uf * sp.Rational(1, lb_method.dim) * (2 + omega_bulk)
 
         result = []
         for direction, w_i in zip(lb_method.stencil, lb_method.weights):

lbmpy_tests/test_force.py

@@ -120,7 +120,7 @@ def test_modes(stencil, force_model):
             return m - tr/m.shape[0]*sp.eye(m.shape[0])
         C = sp.Rational(1,2) * (2 + omega_s) * (traceless(sp.Matrix(u) * sp.Matrix(F).transpose()) + \
                                                 traceless(sp.Matrix(F) * sp.Matrix(u).transpose())) + \
-            sp.Rational(1,3) * (2 + omega_b) * sp.Matrix(u).dot(F) * sp.eye(method.dim)
+            sp.Rational(1,method.dim) * (2 + omega_b) * sp.Matrix(u).dot(F) * sp.eye(method.dim)
 
         subs = {sp.Symbol(chr(ord("x")+i)) * sp.Symbol(chr(ord("x")+j)) : C[i,j]
                 for i in range(dim) for j in range(dim)}
@@ -133,6 +133,22 @@ def test_modes(stencil, force_model):
             else:
                 assert diff == 0 # difference should be zero
 
+        ff = sp.Matrix(method.force_model(method))
+        # Check eq. 4.53a from schiller2008thermal
+        assert sp.simplify(sum(ff)) == 0
+        # Check eq. 4.53b from schiller2008thermal
+        assert [sp.simplify(sum(ff[i] * stencil[i][j] for i in range(len(stencil)))) for j in range(dim)] == F
+        # Check eq. 4.61a from schiller2008thermal
+        ref = (2 + omega_s)/2 * (traceless(sp.Matrix(u) * sp.Matrix(F).transpose()) + \
+                                 traceless(sp.Matrix(F) * sp.Matrix(u).transpose()))
+        s = sp.zeros(dim)
+        for i in range(0, len(stencil)):
+            s += ff[i] * traceless(sp.Matrix(stencil[i]) * sp.Matrix(stencil[i]).transpose())
+        assert sp.simplify(s-ref) == sp.zeros(dim)
+        # Check eq. 4.61b from schiller2008thermal
+        assert sp.simplify(sum(ff[i] * stencil[i][a]**2 for i in range(len(stencil)) for a in range(dim))
+                           - (2+omega_b)*sp.Matrix(u).dot(F)) == 0
+
         # All other moments should be zero
         assert list(force_moments[dim+1+num_stresses:]) == [0] * (len(stencil)-(dim+1+num_stresses))
     elif force_model == "simple":