def Error_test_Momentum(self, mu):
t_sym = syp.symbols("t_sym")
fakeSolnx = syp.exp(-t_sym) * self.phi[0]
fakeSolny = syp.exp(-t_sym) * self.phi[0]
fx = syp.lambdify([self.x, self.y, t_sym], fakeSolnx, "numpy")
fy = syp.lambdify([self.x, self.y, t_sym], fakeSolny, "numpy")
SourceTermx = syp.diff(fakeSolnx, t_sym) + fakeSolnx * syp.diff(
fakeSolnx, self.x) + fakeSolny * syp.diff(
fakeSolnx,
self.y) - mu * (syp.diff(syp.diff(fakeSolnx, self.x), self.x) +
syp.diff(syp.diff(fakeSolnx, self.y), self.y))
SourceTermy = syp.diff(fakeSolny, t_sym) + fakeSolnx * syp.diff(
fakeSolny, self.x) + fakeSolny * syp.diff(
fakeSolny,
self.y) - mu * (syp.diff(syp.diff(fakeSolny, self.x), self.x) +
syp.diff(syp.diff(fakeSolny, self.y), self.y))
source_x = syp.MutableDenseNDimArray(zeros((1, self.N))[0])
source_y = syp.MutableDenseNDimArray(zeros((1, self.N))[0])
self.a_error[0, 0] = 1.0
self.b_error[0, 0] = 1.0
for i in range(self.N):
source_x[i] = integrate(SourceTermx * self.phi[i] * self.orthW,
self.wx, self.x_int, self.wy, self.y_int)
source_y[i] = integrate(SourceTermy * self.phi[i] * self.orthW,
self.wx, self.x_int, self.wy, self.y_int)
return fx, fy, syp.lambdify([t_sym], source_x), syp.lambdify([t_sym],
source_y)
def AssembleNonLinearTerms(self):
print("Assembling Non-Linear terms...")
starttime = ti.time()
i = 0
w = self.w
phi = self.phi
dxphi = self.dxphi
dyphi = self.dyphi
A = syp.MutableDenseNDimArray(zeros((self.N, self.N)))
B = syp.MutableDenseNDimArray(zeros((self.N, self.N)))
while i < self.N:
weight_func = w[i]
for j in range(self.N):
phi1 = phi[j]
for k in range(self.N):
A[i, j] += self.a_sym[k] * integrate(
weight_func * phi1 * dxphi[k] * self.orthW, self.wx,
self.x_int, self.wy, self.y_int)
B[i, j] += self.a_sym[k] * integrate(
weight_func * phi1 * dyphi[k] * self.orthW, self.wx,
self.x_int, self.wy, self.y_int)
i += 1
print("Done")
print("that took:",
ti.time() - starttime, "s")
return syp.lambdify([self.a_sym], A), syp.lambdify([self.a_sym], B)
def AssembleLinearTerms(self):
print("Assembling Linear terms...")
L1 = zeros((self.N, self.N))
L2 = zeros((self.N, self.N))
L3 = zeros((self.N, self.N))
L4 = zeros((self.N, self.N))
L5 = zeros((self.N, self.N))
Lp1 = zeros((self.N, self.N))
Lp2 = zeros((self.N, self.N))
Lp3 = zeros((self.N, self.N))
starttime = ti.time()
for i in range(self.N):
phi1 = self.w[i]
for j in range(self.N):
phi2 = self.phi[j]
dxphi2 = self.dxphi[j]
dyphi2 = self.dyphi[j]
# x & y momentum:
L1[i, j] = integrate(phi1 * phi2 * self.orthW, self.wx,
self.x_int, self.wy, self.y_int)
# Left side of equation phi_i*phi_j
L2[i, j] = integrate(phi1 * self.dxphi_p[j] * self.orthW,
self.wx, self.x_int, self.wy, self.y_int)
# Grad P dphi_i/dx*phi_j
L3[i,
j] = integrate(phi1 * syp.diff(dxphi2, self.x) * self.orthW,
self.wx, self.x_int, self.wy, self.y_int)
# Visc terms d2phi_i/dx*phi_j
L4[i,
j] = integrate(phi1 * syp.diff(dyphi2, self.y) * self.orthW,
self.wx, self.x_int, self.wy, self.y_int)
# Visc terms d2phi_i/dy*phi_j
L5[i, j] = integrate(phi1 * self.dyphi_p[j] * self.orthW,
self.wx, self.x_int, self.wy, self.y_int)
# Grad P dphi_i/dy*phi_j
# Pressure
Lp1[i,
j] = integrate(self.phi_p[i] * self.phi_p[j] * self.orthW,
self.wx, self.x_int, self.wy, self.y_int)
Lp2[i, j] = integrate(self.phi_p[i] * dxphi2 * self.orthW,
self.wx, self.x_int, self.wy, self.y_int)
Lp3[i, j] = integrate(self.phi_p[i] * dyphi2 * self.orthW,
self.wx, self.x_int, self.wy, self.y_int)
Pu = inv(L1).dot(L2)
Pv = inv(L1).dot(L5)
Al = inv(L1).dot(L3 + L4)
Lup = inv(Lp1).dot(Lp2)
Lvp = inv(Lp1).dot(Lp3)
print("Done")
print("that took:",
ti.time() - starttime, "s")
# Returns phi_i*phi_j, dphi_i/dx*phi_j, dphi_i/dy*phi_j
return L1, Pu, Pv, Al, Lp1, Lup, Lvp
def Error_test_Pressure(self):
t_sym = syp.symbols("t_sym")
fakeSoln = syp.exp(-t_sym) * self.phi_p[0]
fP = syp.lambdify([self.x, self.y, t_sym], fakeSoln, "numpy")
SourceTerm = syp.diff(fakeSoln, t_sym)
source = syp.MutableDenseNDimArray(zeros((1, self.N))[0])
self.p_error[0, 0] = 1
for i in range(self.N):
source[i] = integrate(SourceTerm * self.phi_p[i] * self.orthW,
self.wx, self.x_int, self.wy, self.y_int)
return fP, syp.lambdify([t_sym], source, "numpy")
def Source(self):
t_sym = syp.symbols("t_sym")
a = 0.0001
SourceTermx = (syp.exp(-t_sym**2 / a**2) + syp.exp(
-(t_sym - 0.3)**2 / a**2) + syp.exp(-(t_sym - 0.6)**2 / a**2)) * (
2 * self.phi[0] + 6.7 * self.phi[1] - 3.5 * self.phi[2] +
1.4 * self.phi[3])
source_x = syp.MutableDenseNDimArray(zeros((1, self.N))[0])
for i in range(self.N):
source_x[i] = integrate(SourceTermx * self.phi[i] * self.orthW,
self.wx, self.x_int, self.wy, self.y_int)
return syp.lambdify([t_sym], source_x, "numpy")
#def SourceTerm(self, t):
# u = self.UV(self.a[:, t], x_mesh, y_mesh);
# v = self.UV(self.b[:, t], x_mesh, y_mesh);
# b = zeros_like(u);
# b[1: -1, 1: -1] = (rho*(1/dt*((u[1: -1, 2:] - u[1: -1, 0: -2])/(2*dx) + (v[2:, 1: -1] - v[0: -2, 1: -1])/(2*dy)) - ((u[1: -1, 2:] - u[1: -1, 0: -2])/(2*dx))**2 -
# 2*((u[2:, 1: -1] - u[0: -2, 1: -1])/(2*dy)*(v[1: -1, 2:] - v[1: -1, 0: -2])/(2*dx)) - ((v[2:, 1: -1] - v[0: -2, 1: -1])/(2*dy))**2));
# return b;
#def Pressure_Update(p, t, iter_max = 50):
# iter = 1;
# b = self.SourceTerm(t);
# while iter <= iter_max:
# pn = p.copy();
# p[1: -1, 1: -1] = (((pn[1: -1, 2:] + pn[1: -1, 0: -2])*dy**2 + (pn[2:, 1: -1] + pn[0: -2, 1: -1])*dx**2)/(2*(dx**2 + dy**2)) -
# dx**2*dy**2/(2*(dx**2 + dy**2))*b[1: -1, 1: -1]);
# # Wall BC
# p[:, -1] = p[:, -2]; # @ x = 1
# p[0, :] = p[1, :]; # @ y = -1
# p[:, 0] = p[:, 1]; # @ x = -1
# p[-1, :] = p[-2, :]; # @ y = 1
# iter += 1
# return p;