def generate_inviscid(path_msh, parent_folder):
single_nodes_X, single_nodes_Y, elements = extract_msh(path_msh)
rs = np.sqrt(single_nodes_X**2 + single_nodes_Y**2)
thetas = np.arctan2(single_nodes_Y, single_nodes_X)
Ur, Utheta, p = [], [], []
for r, theta in zip(rs, thetas):
if r == 0:
Ur.append(0)
Utheta.append(0)
p.append(0)
else:
Ur.append((1 - (0.5 / r)**2) * np.cos(theta))
Utheta.append((1 + (0.5 / r)**2) * np.sin(theta))
p.append(2 * (0.5 / r)**2 * np.cos(2 * theta) - (0.5 / r)**4)
Ur = np.array(Ur)
Utheta = np.array(Utheta)
p = np.array(p)
U = Ur * np.cos(thetas) - Utheta * np.sin(thetas)
V = Ur * np.sin(thetas) - Utheta * np.cos(thetas)
nodes_X, nodes_Y = np.array([]), np.array([])
Us, Vs, ps = np.array([]), np.array([]), np.array([])
Nt = 101
times = np.linspace(0, 1, Nt)
for t in times:
nodes_X = np.vstack([nodes_X, single_nodes_X
]) if nodes_X.size else single_nodes_X
nodes_Y = np.vstack([nodes_Y, single_nodes_Y
]) if nodes_Y.size else single_nodes_Y
Us = np.vstack([Us, U]) if Us.size else U
Vs = np.vstack([Vs, V]) if Vs.size else V
ps = np.vstack([ps, p]) if ps.size else p
Re, Ur = 1e+6, 0.
flow = Flow()
flow.Re, flow.Ur = Re, Ur
flow.times = times
flow.nodes_X, flow.nodes_Y = nodes_X, nodes_Y
flow.Us, flow.Vs, flow.ps = Us, Vs, ps
write_flow(flow, parent_folder + 'flows/potential')
find_neighbors(elements)
write_elements(elements, parent_folder + 'elements/potential')
write_geometries(
np.array([[
5, 407, 404, 408, 405, 409, 406, 410, 6, 414, 411, 415, 412, 416,
413, 417
]]), parent_folder + 'geometries/potential')
def generate_periodic(path_msh, parent_folder):
single_nodes_X, single_nodes_Y, elements = extract_msh(path_msh)
d = np.max(single_nodes_Y) - np.min(single_nodes_Y)
Nt = 101
times = np.linspace(0, 1, Nt)
period = 0.25
w = 2 * np.pi / period
# U = U0*cos(wt) with U0 = 1
# Navier-Stokes, uniform:
# rho dU/dt + 0 = - dp/dx with rho = 1
# dp/dx = rhoU0*w*sin(wt)
# p = p0 + rhoU0*w*sin(wt) with p0 = 0
nodes_X, nodes_Y = np.array([]), np.array([])
Us, Vs, ps = np.array([]), np.array([]), np.array([])
for t in times:
nodes_X = np.vstack([nodes_X, single_nodes_X
]) if nodes_X.size else single_nodes_X
nodes_Y = np.vstack([nodes_Y, single_nodes_Y
]) if nodes_Y.size else single_nodes_Y
U = 0 * nodes_X + np.cos(w * t)
V = 0 * nodes_X
p = 0 * nodes_X + w * np.sin(w * t)
Us = np.vstack([Us, U]) if Us.size else U
Vs = np.vstack([Vs, V]) if Vs.size else V
ps = np.vstack([ps, p]) if ps.size else p
Re, Ur = 1 * 1 * d / 1e-6, np.inf
flow = Flow()
flow.Re, flow.Ur = Re, Ur
flow.times = times
flow.nodes_X, flow.nodes_Y = nodes_X, nodes_Y
flow.Us, flow.Vs, flow.ps = Us, Vs, ps
write_flow(flow, parent_folder + 'flows/periodic')
find_neighbors(elements)
write_elements(elements, parent_folder + 'elements/periodic')
write_geometries(np.array([]), parent_folder + 'geometries/periodic')
def generate_poiseuille(path_msh, parent_folder):
single_nodes_X, single_nodes_Y, elements = extract_msh(path_msh)
d = np.max(single_nodes_Y) - np.min(single_nodes_Y)
y_middle = np.min(single_nodes_Y) + d / 2
n_nodes = len(single_nodes_X)
mu = 1e-3
p = 2 * mu * single_nodes_X
U = d**2 / 4 - (single_nodes_Y - y_middle)**2
V = np.zeros(n_nodes)
nodes_X, nodes_Y = np.array([]), np.array([])
Us, Vs, ps = np.array([]), np.array([]), np.array([])
Nt = 101
times = np.linspace(0, 1, Nt)
for t in times:
nodes_X = np.vstack([nodes_X, single_nodes_X
]) if nodes_X.size else single_nodes_X
nodes_Y = np.vstack([nodes_Y, single_nodes_Y
]) if nodes_Y.size else single_nodes_Y
Us = np.vstack([Us, U]) if Us.size else U
Vs = np.vstack([Vs, V]) if Vs.size else V
ps = np.vstack([ps, p]) if ps.size else p
Re, Ur = 1e-3 * 1 * d / mu, np.inf # Reynolds number and reduced velocity are not
# defined in the Hagen-Poiseuille problem
flow = Flow()
flow.Re, flow.Ur = Re, Ur
flow.times = times
flow.nodes_X, flow.nodes_Y = nodes_X, nodes_Y
flow.Us, flow.Vs, flow.ps = Us, Vs, ps
write_flow(flow, parent_folder + 'flows/poiseuille')
find_neighbors(elements)
write_elements(elements, parent_folder + 'elements/poiseuille')
write_geometries(np.array([]), parent_folder + 'geometries/poiseuille')