def hex_couette():
m, n = 6, 12
G, (l, r, t, b) = gds.hexagonal_lattice(m, n, with_boundaries=True)
faces, outer_face = gds.embedded_faces(G)
contractions = {}
for j in range(1, 2*m+1):
G = nx.algorithms.minors.contracted_nodes(G, (0, j), (n, j))
contractions[(n, j)] = (0, j)
nx.set_node_attributes(G, None, 'contraction')
rendered_faces = set()
for i, face in enumerate(faces):
face = list(face)
modified = False
for j, node in enumerate(face):
if node in contractions:
n_l = contractions[node] # identified
face[j] = n_l
faces[i] = tuple(face)
modified = True
if not modified:
rendered_faces.add(i)
G.faces = faces
G.rendered_faces = np.array(sorted(list(rendered_faces)), dtype=np.intp) # Hacky
pressure, velocity = navier_stokes(G, viscosity=1., density=1e-2)
vel = 1.0
def walls(e):
if (e[0][1] == e[1][1] == 0) and (e[0][0] == e[1][0] - 1):
return vel
elif e in t.edges or e == ((0, 2*m), (n, 2*m+1)):
return 0.0
return None
velocity.set_constraints(dirichlet=walls)
return pressure, velocity
def square_edge_diffusion():
m, n = 10, 10
G, (l, r, t, b) = gds.square_lattice(n, m, with_boundaries=True)
faces, outer_face = gds.embedded_faces(G)
for j in range(m):
G.add_edge((n - 1, j), (0, j))
aux_faces = [((n - 1, j), (0, j), (0, j + 1), (n - 1, j + 1))
for j in range(m - 1)]
G.faces = faces + aux_faces # Hacky
G.rendered_faces = np.array(range(len(faces)), dtype=np.intp) # Hacky
v = gds.edge_gds(G)
v.set_evolution(dydt=lambda t, y: v.laplacian(y))
velocity = 1.0
def boundary(e):
if e in b.edges:
return velocity
elif e == ((0, 0), (m - 1, 0)):
return -velocity
elif e in t.edges or e == ((0, n - 1), (m - 1, n - 1)):
return 0.0
return None
v.set_constraints(dirichlet=boundary)
return v
def tri_couette(): m, n = 10, 20 G, (l, r, t, b) = gds.triangular_lattice(m, n, with_boundaries=True) faces, outer_face = gds.embedded_faces(G) for j in range(m+1): G = nx.algorithms.minors.contracted_nodes(G, (0, j), ((n + 1) // 2, j)) rendered_faces = set() r_nodes = set(r.nodes()) for i, face in enumerate(faces): face = list(face) modified = False for j, node in enumerate(face): if node in r_nodes: n_l = (0, node[1]) # identified face[j] = n_l faces[i] = tuple(face) modified = True if not modified: rendered_faces.add(i) G.faces = faces G.rendered_faces = np.array(sorted(list(rendered_faces)), dtype=np.intp) # Hacky pressure, velocity = navier_stokes(G, viscosity=1., density=1e-2) vel = 1.0 def walls(e): if e in b.edges: return vel elif e == ((0, 0), (n//2-1, 0)): return -vel elif e in t.edges or e == ((0, m), (n//2-1, m)): return 0.0 return None velocity.set_constraints(dirichlet=walls) return pressure, velocity
def tri_couette_ivp(viscosity, density): m, n = 10, 20 G, (l, r, t, b) = gds.triangular_lattice(m, n, with_boundaries=True, with_lattice_components=True) lcomps = G.lattice_components faces, outer_face = gds.embedded_faces(G) for j in range(m+1): G = nx.algorithms.minors.contracted_nodes(G, (0, j), ((n + 1) // 2, j)) rendered_faces = set() r_nodes = set(r.nodes()) for i, face in enumerate(faces): face = list(face) modified = False for j, node in enumerate(face): if node in r_nodes: n_l = (0, node[1]) # identified face[j] = n_l faces[i] = tuple(face) modified = True if not modified: rendered_faces.add(i) G.faces = faces G.rendered_faces = np.array(sorted(list(rendered_faces)), dtype=np.intp) # Hacky # hacky nodes, edges = set(G.nodes()), set(G.edges()) for comp in lcomps.values(): comp.remove_nodes_from(set(comp.nodes()) - nodes) comp.remove_edges_from(set(comp.edges() - edges)) G.lattice_components = lcomps pressure, velocity = navier_stokes(G, viscosity=viscosity, density=density) vel = 1.0 def walls(e): if e[0][1] == e[1][1] == m//2: if e == ((0, 0), (n//2-1, 0)): return -vel return vel return 0 velocity.set_initial(y0=walls) return pressure, velocity
def sq_couette(): m, n = 11, 10 G, (l, r, t, b) = gds.square_lattice(m, n, with_boundaries=True) faces, outer_face = gds.embedded_faces(G) for j in range(m): G.add_edge((n-1, j), (0, j)) aux_faces = [((n-1, j), (0, j), (0, j+1), (n-1, j+1)) for j in range(m-1)] G.faces = faces + aux_faces # Hacky G.rendered_faces = np.array(range(len(faces)), dtype=np.intp) # Hacky pressure, velocity = navier_stokes(G, viscosity=1., density=1e-2) vel = 1.0 def walls(e): if e in t.edges or e == ((0, m-1), (n-1, m-1)): return 0 elif e in b.edges: return vel elif e == ((0, 0), (n-1, 0)): return -vel return None velocity.set_constraints(dirichlet=walls) return pressure, velocity
def hex_edge_diffusion():
m, n = 10, 20
G, (l, r, t, b) = gds.hexagonal_lattice(m, n, with_boundaries=True)
faces, outer_face = gds.embedded_faces(G)
contractions = {}
for j in range(1, 2 * m + 1):
G = nx.algorithms.minors.contracted_nodes(G, (0, j), (n, j))
contractions[(n, j)] = (0, j)
nx.set_node_attributes(G, None, 'contraction')
rendered_faces = set()
for i, face in enumerate(faces):
face = list(face)
modified = False
for j, node in enumerate(face):
if node in contractions:
n_l = contractions[node] # identified
face[j] = n_l
faces[i] = tuple(face)
modified = True
if not modified:
rendered_faces.add(i)
G.faces = faces
G.rendered_faces = np.array(sorted(list(rendered_faces)),
dtype=np.intp) # Hacky
# pdb.set_trace()
v = gds.edge_gds(G)
v.set_evolution(dydt=lambda t, y: v.laplacian(y))
velocity = 1.0
def boundary(e):
if (e[0][1] == e[1][1] == 0) and (e[0][0] == e[1][0] - 1):
return velocity
elif e in t.edges or e == ((0, 2 * m), (n, 2 * m + 1)):
return 0.0
return None
v.set_constraints(dirichlet=boundary)
return v
def sq_couette_ivp(viscosity, density): m, n = 11, 10 G, (l, r, t, b) = gds.square_lattice(m, n, with_boundaries=True, with_lattice_components=True) faces, outer_face = gds.embedded_faces(G) for j in range(m): G.add_edge((n-1, j), (0, j)) # for i in range(n): # G.add_edge((i, 0), (i, m-1)) aux_faces = [((n-1, j), (0, j), (0, j+1), (n-1, j+1)) for j in range(m-1)] # aux_faces += [((i, 0), (i, m-1), (i+1, m-1), (i+1, 0)) for i in range(n-1)] G.faces = faces + aux_faces # Hacky G.rendered_faces = np.array(range(len(faces)), dtype=np.intp) # Hacky pressure, velocity = navier_stokes(G, viscosity=viscosity, density=density) vel = 1.0 def walls(e): if e[0][1] == e[1][1] == m//2: if e[0][0] == 0 and e[1][0] == n-1: return -vel return vel return 0 velocity.set_initial(y0=walls) return pressure, velocity
def tri_edge_diffusion():
m, n = 10, 20
G, (l, r, t, b) = gds.triangular_lattice(m, n, with_boundaries=True)
faces, outer_face = gds.embedded_faces(G)
for j in range(m + 1):
G = nx.algorithms.minors.contracted_nodes(G, (0, j), ((n + 1) // 2, j))
rendered_faces = set()
r_nodes = set(r.nodes())
for i, face in enumerate(faces):
face = list(face)
modified = False
for j, node in enumerate(face):
if node in r_nodes:
n_l = (0, node[1]) # identified
face[j] = n_l
faces[i] = tuple(face)
modified = True
if not modified:
rendered_faces.add(i)
G.faces = faces
G.rendered_faces = np.array(sorted(list(rendered_faces)),
dtype=np.intp) # Hacky
v = gds.edge_gds(G)
v.set_evolution(dydt=lambda t, y: v.laplacian(y))
velocity = 1.0
def boundary(e):
if e in b.edges:
return velocity
elif e == ((0, 0), (n // 2 - 1, 0)):
return -velocity
elif e in t.edges or e == ((0, m), (n // 2 - 1, m)):
return 0.0
return None
v.set_constraints(dirichlet=boundary)
return v