def test_1D_plug(version):
def q(x,y):
return ones((len(x),len(y)))
def V(x,y):
return zeros((len(x), len(y)))
if version == "scalar":
def I(x,y):
return 0 if abs(x-xc) > sigma else 2
else:
def I(xv, yv):
Iv = zeros((len(xv), len(yv)))
for i in range(len(xv)):
for j in range(len(yv)):
if abs(xv[j, i] - xc) > sigma:
Iv[i, j] = 0
else:
Iv[i, j] = 2
return Iv
def f(x,y,t):
return zeros((len(x), len(y)))
E, u, dx = solver(Lx, Ly, Nx, Ny, T, dt, c, I, q, V, f, b, version, oneD=True)
def test_constant(version):
def q(x, y):
return ones((len(x), len(y))) * 0.8
def V(x, y):
return zeros((len(x), len(y)))
def I(x, y):
return 1.2
def f(x, y, t):
return zeros((len(x), len(y)))
E, u, dx = solver(Lx,
Ly,
Nx,
Ny,
T,
dt,
c,
I,
q,
V,
f,
b,
version,
make_plot=False)
if version == "scalar":
print u
else:
print u[1:-1, 1:-1]
def run_Gaussian_flathill(version):
def I(x, y):
"""Gaussian peak at (0, Ly/2)."""
# return 2*exp(-0.5*((x-Lx/2.0)/(sigma))**2 - 0.5*((y-Ly/2.0)/(sigma))**2)
return height * exp(-0.5 * ((x) / (sigma))**2 - 0.5 * ((y - Ly / 2.0) /
(sigma))**2)
def B(x, y):
return x - H0
def V(x, y):
return ones((len(x), len(y))) * factor
def q(x, y):
return g * (H0 - B(x, y))
def f(x, y, t):
return zeros((len(x), len(y)))
E, u, dx = solver(Lx,
Ly,
Nx,
Ny,
T,
dt,
c,
I,
q,
V,
f,
b,
version,
B=B,
make_plot=True)
def test_standing_wave(version, w, Nx):
Ny = Nx
def q(x, y):
return ones((len(x), len(y))) * q_const
def f(x, y, t):
return exp(-b * t) * cos(cx * x) * cos(cy * y) * (
cos(w * t) *
(q_const * cx**2 + q_const * cy**2 - w**2) + b * w * sin(w * t))
def I(x, y):
return cos(mx * x * pi / Lx) * cos(my * y * pi / Ly)
def V(x, y):
return -b * cos(mx * x * pi / Lx) * cos(my * y * pi / Ly)
E_list, u, dx = solver(Lx,
Ly,
Nx,
Ny,
T,
dt,
c,
I,
q,
V,
f,
b,
version,
w=w,
exact=exact_standing_wave,
make_plot=False)
return E_list, dx
def test_standing_wave(version, w, Nx):
Ny = Nx
def q(x,y):
return ones((len(x),len(y))) * q_const
def f(x,y,t):
return exp(-b*t)*cos(cx*x)*cos(cy*y)*(cos(w*t)*(q_const*cx**2 + q_const*cy**2 - w**2) + b*w*sin(w*t))
def I(x,y):
return cos(mx*x*pi/Lx)*cos(my*y*pi/Ly)
def V(x,y):
return -b*cos(mx*x*pi/Lx)*cos(my*y*pi/Ly)
E_list, u, dx = solver(Lx, Ly, Nx, Ny, T, dt, c, I, q, V, f, b, version, w=w, exact=exact_standing_wave, make_plot=False)
return E_list, dx
def test_constant(version):
def q(x, y):
return ones((len(x), len(y))) * 0.8
def V(x, y):
return zeros((len(x), len(y)))
def I(x, y):
return 1.2
def f(x, y, t):
return zeros((len(x), len(y)))
E, u, dx = solver(Lx, Ly, Nx, Ny, T, dt, c, I, q, V, f, b, version, make_plot=False)
if version == "scalar":
print u
else:
print u[1:-1, 1:-1]
def run_Gaussian_flathill(version):
def I(x,y):
"""Gaussian peak at (0, Ly/2)."""
# return 2*exp(-0.5*((x-Lx/2.0)/(sigma))**2 - 0.5*((y-Ly/2.0)/(sigma))**2)
return height*exp(-0.5*((x)/(sigma))**2 - 0.5*((y-Ly/2.0)/(sigma))**2)
def B(x,y):
return x-H0
def V(x,y):
return ones((len(x),len(y)))*factor
def q(x,y):
return g*(H0-B(x,y))
def f(x,y,t):
return zeros((len(x),len(y)))
E, u, dx = solver(Lx, Ly, Nx, Ny, T, dt, c, I, q, V, f, b, version, B=B, make_plot=True)
def test_1D_plug(version):
def q(x, y):
return ones((len(x), len(y)))
def V(x, y):
return zeros((len(x), len(y)))
if version == "scalar":
def I(x, y):
return 0 if abs(x - xc) > sigma else 2
else:
def I(xv, yv):
Iv = zeros((len(xv), len(yv)))
for i in range(len(xv)):
for j in range(len(yv)):
if abs(xv[j, i] - xc) > sigma:
Iv[i, j] = 0
else:
Iv[i, j] = 2
return Iv
def f(x, y, t):
return zeros((len(x), len(y)))
E, u, dx = solver(Lx,
Ly,
Nx,
Ny,
T,
dt,
c,
I,
q,
V,
f,
b,
version,
oneD=True)
def test_manufactured_solution(version, w, Nx):
Ny = Nx
def q(x, y):
return x * y
def f(x, y, t):
f_val = exp(-b*t)*(cos(cx*x)*cos(cy*y)*(-w**2*cos(w*t) + b*w*sin(w*t)) + \
cx*y*cos(cy*y)*cos(w*t)*(cx*x*cos(cx*x) + sin(cy*y)) + \
cy*x*cos(cx*x)*cos(w*t)*(cy*y*cos(cy*y) + sin(cx*x)))
return f_val
def I(x, y):
if version == "scalar":
return m.cos(cx * x) * m.cos(cy * y)
else:
return cos(cx * x) * cos(cy * y)
def V(x, y):
return -b * cos(cx * x) * cos(cy * y)
E_list, u, dx = solver(Lx,
Ly,
Nx,
Ny,
T,
dt,
c,
I,
q,
V,
f,
b,
version,
w=w,
exact=exact_manufactured_solution,
make_plot=False)
return E_list, dx
def test_manufactured_solution(version, w, Nx):
Ny = Nx
def q(x,y):
return x*y
def f(x,y,t):
f_val = exp(-b*t)*(cos(cx*x)*cos(cy*y)*(-w**2*cos(w*t) + b*w*sin(w*t)) + \
cx*y*cos(cy*y)*cos(w*t)*(cx*x*cos(cx*x) + sin(cy*y)) + \
cy*x*cos(cx*x)*cos(w*t)*(cy*y*cos(cy*y) + sin(cx*x)))
return f_val
def I(x,y):
if version=="scalar":
return m.cos(cx*x)*m.cos(cy*y)
else:
return cos(cx*x)*cos(cy*y)
def V(x,y):
return -b*cos(cx*x)*cos(cy*y)
E_list, u, dx = solver(Lx, Ly, Nx, Ny, T, dt, c, I, q, V, f, b, version, w=w, exact=exact_manufactured_solution, make_plot=False)
return E_list, dx
