Fixed 3D-VoF signs and added testcase

pystencils/fd/finitevolumes.py

@@ -15,7 +15,7 @@ class FVM1stOrder:
         flux: a list of sympy expressions that specify the flux, one for each cartesian direction
         source: a list of sympy expressions that specify the source
     """
-    def __init__(self, field: ps.field.Field, flux=0, source=0):
+    def __init__(self, field: ps.field.Field, flux=0, source=0, flux_scaling: bool = False):
         def normalize(f, shape):
             shape = tuple(s for s in shape if s != 1)
             if not shape:
@@ -30,6 +30,7 @@ class FVM1stOrder:
         self.dim = self.c.spatial_dimensions
         self.j = normalize(flux, (self.dim, ) + self.c.index_shape)
         self.q = normalize(source, self.c.index_shape)
+        self.flux_scaling = flux_scaling
 
     def discrete_flux(self, flux_field: ps.field.Field):
         """Return a list of assignments for the discrete fluxes
@@ -85,14 +86,22 @@ class FVM1stOrder:
             for i in range(1, self.dim):
                 directional_flux += fluxes[i] * int(neighbor[i])
             discrete_flux = discretize(directional_flux, neighbor)
+            if self.flux_scaling:
+                discrete_flux /= sp.Matrix(neighbor).norm()
             discrete_fluxes.append(discrete_flux)
             
+        if self.flux_scaling:
+            A0 = sum([sp.Matrix(ps.stencil.direction_string_to_offset(d)).norm()
+                      for d in flux_field.staggered_stencil]) / self.dim
+        else:
+            A0 = 1
+
         if flux_field.index_dimensions > 1:
-            return [ps.Assignment(lhs, rhs)
+            return [ps.Assignment(lhs, rhs / A0)
                     for i, d in enumerate(flux_field.staggered_stencil) if discrete_fluxes[i]
                     for lhs, rhs in zip(flux_field.staggered_vector_access(d), sp.simplify(discrete_fluxes[i]))]
         else:
-            return [ps.Assignment(flux_field.staggered_access(d), sp.simplify(discrete_fluxes[i]))
+            return [ps.Assignment(flux_field.staggered_access(d), sp.simplify(discrete_fluxes[i] / A0))
                     for i, d in enumerate(flux_field.staggered_stencil)]
 
     def discrete_source(self):
@@ -185,10 +194,11 @@ class FVM1stOrder:
         neighbors = flux_field.staggered_stencil + [ps.stencil.inverse_direction_string(d)
                                                     for d in flux_field.staggered_stencil]
         divergence = flux_field.staggered_vector_access(neighbors[0]) / \
-            sp.Matrix(ps.stencil.direction_string_to_offset(neighbors[0])).norm()
+            (sp.Matrix(ps.stencil.direction_string_to_offset(neighbors[0])).norm() if not self.flux_scaling else 1)
         for d in neighbors[1:]:
             divergence += flux_field.staggered_vector_access(d) / \
-                sp.Matrix(ps.stencil.direction_string_to_offset(d)).norm()
+                (sp.Matrix(ps.stencil.direction_string_to_offset(d)).norm() if not self.flux_scaling else 1)
+        if not self.flux_scaling:
             A0 = sum([sp.Matrix(ps.stencil.direction_string_to_offset(d)).norm()
                       for d in flux_field.staggered_stencil]) / self.dim
             divergence /= A0
@@ -217,19 +227,23 @@ def VOF(j: ps.field.Field, v: ps.field.Field, ρ: ps.field.Field):
         c = ps.stencil.direction_string_to_offset(neighbor)
         v1 = v.neighbor_vector(c)
 
+        # sign flips if exactly one directional offset is 1
+        it = iter(c == 1)
+        sign = -1 if any(it) and not any(it) else 1
+
         # going out
         cond = sp.And(*[sp.Or(c[i] * v0[i] > 0, c[i] == 0) for i in range(len(v0))])
         overlap1 = [1 - sp.Abs(v0[i]) for i in range(len(v0))]
-        overlap2 = [c[i] * v0[i] for i in range(len(v0))]
+        overlap2 = [-v0[i] for i in range(len(v0))]
         overlap = sp.Mul(*[(overlap1[i] if c[i] == 0 else overlap2[i]) for i in range(len(v0))])
-        fluxes[d].append(ρ.center_vector * overlap * sp.Piecewise((1, cond), (0, True)))
+        fluxes[d].append(sign * ρ.center_vector * overlap * sp.Piecewise((1, cond), (0, True)))
 
         # coming in
         cond = sp.And(*[sp.Or(c[i] * v1[i] < 0, c[i] == 0) for i in range(len(v1))])
         overlap1 = [1 - sp.Abs(v1[i]) for i in range(len(v1))]
         overlap2 = [v1[i] for i in range(len(v1))]
         overlap = sp.Mul(*[(overlap1[i] if c[i] == 0 else overlap2[i]) for i in range(len(v1))])
-        fluxes[d].append(ρ.neighbor_vector(c) * overlap * sp.Piecewise((1, cond), (0, True)))
+        fluxes[d].append(-sign * ρ.neighbor_vector(c) * overlap * sp.Piecewise((1, cond), (0, True)))
 
     for i, ff in enumerate(fluxes):
         fluxes[i] = ff[0]

pystencils_tests/test_fvm.py

@@ -12,9 +12,11 @@ def test_advection_diffusion(dim: int):
         domain_size = (32, 32)
         flux_neighbors = 4
     elif dim == 3:
-        domain_size = (16, 16, 16)
+        domain_size = (32, 32, 32)
         flux_neighbors = 13
 
+    domain_center = [dom // 2 for dom in domain_size]
+
     dh = ps.create_data_handling(
         domain_size=domain_size, periodicity=True, default_target='cpu')
 
@@ -24,13 +26,13 @@ def test_advection_diffusion(dim: int):
     velocity_field = dh.add_array('v', values_per_cell=dim)
 
     D = 0.0666
-    time = 200
+    time = 300
 
     def grad(f):
         return sp.Matrix([ps.fd.diff(f, i) for i in range(dim)])
 
     flux_eq = - D * grad(n_field)
-    fvm_eq = ps.fd.FVM1stOrder(n_field, flux=flux_eq)
+    fvm_eq = ps.fd.FVM1stOrder(n_field, flux=flux_eq, flux_scaling=True)
 
     vof_adv = ps.fd.VOF(j_field, velocity_field, n_field)
 
@@ -47,20 +49,21 @@ def test_advection_diffusion(dim: int):
 
     sync_conc = dh.synchronization_function([n_field.name])
 
-    # analytical density calculation
+    # analytical density calculation with first eight neighbors in square domain
     def density(pos: np.ndarray, time: int):
-        return (4 * np.pi * D * time)**(-1.5) * \
-            np.exp(-np.sum(np.square(pos), axis=dim) / (4 * D * time))
+        return sum((4 * np.pi * D * time) ** (-dim / 2) * np.exp(
+            -np.sum(np.square(pos + np.asarray(shift)), axis=dim) / (4 * D * time))
+                   for shift in product([0, dh.shape[0], -dh.shape[0]], repeat=dim))
 
     pos = np.zeros((*domain_size, dim))
     xpos = np.arange(-domain_size[0] // 2, domain_size[0] // 2)
     ypos = np.arange(-domain_size[1] // 2, domain_size[1] // 2)
 
     if dim == 2:
-        pos[..., 1], pos[..., 0] = np.meshgrid(xpos, ypos)
+        pos[..., 0], pos[..., 1] = np.meshgrid(xpos, ypos, indexing='ij')
     elif dim == 3:
         zpos = np.arange(-domain_size[2] // 2, domain_size[2] // 2)
-        pos[..., 2], pos[..., 1], pos[..., 0] = np.meshgrid(xpos, ypos, zpos)
+        pos[..., 0], pos[..., 1], pos[..., 2] = np.meshgrid(xpos, ypos, zpos, indexing='ij')
 
     def run(velocity: np.ndarray, time: int):
         print(f"{velocity}, {time}")
@@ -71,8 +74,7 @@ def test_advection_diffusion(dim: int):
         for i in range(dim):
             dh.fill(velocity_field.name, velocity[i], i, ghost_layers=True, inner_ghost_layers=True)
         dh.fill(n_field.name, 0)
-        dh.fill(n_field.name, 1, slice_obj=ps.make_slice[[
-                dom // 2 for dom in domain_size]])
+        dh.fill(n_field.name, 1, slice_obj=ps.make_slice[domain_center])
 
         sync_conc()
         for i in range(time):
@@ -80,17 +82,23 @@ def test_advection_diffusion(dim: int):
             dh.run_kernel(pde_kernel)
             sync_conc()
 
-        calc_density = density(pos - velocity * time, time)
+        simulation_density = dh.gather_array(n_field.name)
+        analytic_density = density(pos - velocity * time, time)
+        peak_position = tuple(int(val) for val in domain_center + velocity * time)
+
+        analytical_maximum = analytic_density[peak_position]
+        relative_maximum_error = np.abs(simulation_density[peak_position] - analytical_maximum) / analytical_maximum
 
-        np.testing.assert_allclose(dh.gather_array(
-            n_field.name), calc_density, atol=1e-2, rtol=0)
+        assert dh.min(n_field.name) >= 0
+        assert relative_maximum_error <= 0.18
+        np.testing.assert_array_equal(np.unravel_index(np.argmax(simulation_density), dh.shape), peak_position)
+        np.testing.assert_allclose(simulation_density, analytic_density, atol=5e-4)
 
-    for vel in product([0, -0.08, 0.08], repeat=dim):
+    for vel in product([0, -0.02, 0.02], repeat=dim):
         run(np.array(vel), time)
 
 
 def test_ek():
-
     # parameters
 
     L = (40, 40)
@@ -112,7 +120,7 @@ def test_ek():
 
     flux_eq = -D * Gradient(c) + D * z * c.center * Gradient(Phi)
 
-    disc = ps.fd.FVM1stOrder(c, flux_eq)
+    disc = ps.fd.FVM1stOrder(c, flux_eq, flux_scaling=False)
     flux_assignments = disc.discrete_flux(j)
     advection_assignments = ps.fd.VOF(j, v, c)
     continuity_assignments = disc.discrete_continuity(j)