def test_1Dsolution(): Lx = 10 Ly = 10 def c(x,y): s = (np.size(x),np.size(y)) c = np.zeros(s) c = c + 1 return c def I(x, y): """Tests the plug wave solution, should be reproduced the exact solution!""" return np.logical_and((np.abs(x) < Lx/2.+1), (np.abs(x) > Lx/2.-1))*1. Nx = 40; Ny = 40; T = 21. x = np.linspace(0, Lx, Nx+1) # mesh points in x dir y = np.linspace(0, Ly, Ny+1) # mesh points in y dir dx = x[1] - x[0] dy = y[1] - y[0] dt = dx X,Y = np.meshgrid(x,y) u_exact = I(X,Y) for version in ['scalar','vectorized']: dt,time, T = bw.solver(I, None, None, c, 0.0, Lx, Ly, Nx, Ny, dt, T, version=version) n = int(T/dt - 5) fname = 'solution_%06d.txt' % n u = np.loadtxt(fname) diff = np.abs(u_exact - u[:,0]).max() mcrtmv(n, dt,Lx,Ly,Nx,Ny,savemovie=True, mvname=version)
def test_quadratic(): """test for convergence rate in manufactured solution""" Lx = 4. Ly = 4. def c(x,y): s = (np.size(x),np.size(y)) c = np.zeros(s) c = c + 1 return c mx = 4.; my = 4.; b = 0.01; omega=np.pi; def u_exact(x,y,t): return np.exp(-b*t)*np.cos(mx*x*np.pi/Lx)*np.cos(my*y*np.pi/Ly)*np.cos(omega*t) def f(x,y,t): return np.exp(-b*t)*np.cos(mx*np.pi*x/Lx)*np.cos(my*np.pi*y/Ly)*(b*omega*np.sin(omega*t) + \ ( - omega*omega + (mx*np.pi/Lx)**2 + (my*np.pi/Ly)**2 )*np.cos(omega*t)) def I(x, y): return np.cos(mx*np.pi*x/Lx)*np.cos(my*np.pi*y/Ly) def V(x,y): return -b*np.cos(mx*np.pi*x/Lx)*np.cos(my*np.pi*y/Ly) Nx = 40; Ny = 40; T = 1.0 dt = 0.01 fac = 1. for version in ['scalar','vectorized']: errorlist=[0,0,0,0] for i in range(3): x = np.linspace(0, Lx, Nx+1); dx = x[1]-x[0] # mesh points in x dir y = np.linspace(0, Ly, Ny+1); dy = y[1]-y[0] # mesh points in y dir dt,time, T2 = bw.solver(I, V, f, c, b, Lx, Ly, Nx, Ny, dt, T, version=version) n = int(T/dt) fname = 'solution_%06d.txt' % n u = np.loadtxt(fname) X,Y = np.meshgrid(x,y) u_ex = u_exact(X,Y,T2) error = np.copy((u_ex-u)**2) error = np.sum(error) error = np.sqrt(error*dx*dy) errorlist[i] = error Nx = Nx*2; Ny = Ny*2; dt = dt/2 ratio1 = errorlist[1]/errorlist[0] ratio2 = errorlist[2]/errorlist[1] nt.assert_almost_equal(ratio1, 0.25, delta=0.06) nt.assert_almost_equal(ratio2, 0.25, delta=0.06)
def test_1Dsolution():
Lx = 10
Ly = 10
def c(x, y):
s = (np.size(x), np.size(y))
c = np.zeros(s)
c = c + 1
return c
def I(x, y):
"""Tests the plug wave solution, should be reproduced the exact solution!"""
return np.logical_and((np.abs(x) < Lx / 2. + 1),
(np.abs(x) > Lx / 2. - 1)) * 1.
Nx = 40
Ny = 40
T = 21.
x = np.linspace(0, Lx, Nx + 1) # mesh points in x dir
y = np.linspace(0, Ly, Ny + 1) # mesh points in y dir
dx = x[1] - x[0]
dy = y[1] - y[0]
dt = dx
X, Y = np.meshgrid(x, y)
u_exact = I(X, Y)
for version in ['scalar', 'vectorized']:
dt, time, T = bw.solver(I,
None,
None,
c,
0.0,
Lx,
Ly,
Nx,
Ny,
dt,
T,
version=version)
n = int(T / dt - 5)
fname = 'solution_%06d.txt' % n
u = np.loadtxt(fname)
diff = np.abs(u_exact - u[:, 0]).max()
mcrtmv(n, dt, Lx, Ly, Nx, Ny, savemovie=True, mvname=version)
def test_constant_solution():
"""compare to the constant solution u = 1.2"""
Lx = 10
Ly = 10
def c(x, y):
s = (np.size(x), np.size(y))
c = np.zeros(s)
c = c + 1
return c
def I(x, y):
"""constant solution u = 1.2, should be exact"""
return 1.2
Nx = 40
Ny = 40
T = 20
u_exact = 1.2 * np.ones((Nx + 1, Ny + 1))
for version in ['scalar', 'vectorized']:
dt, time, T2 = bw.solver(I,
None,
None,
c,
0.0,
Lx,
Ly,
Nx,
Ny,
0.1,
T,
version=version)
n = int(T / dt - 1)
fname = 'solution_%06d.txt' % n
u = np.loadtxt(fname)
diff = np.abs(u_exact - u).max()
nt.assert_almost_equal(diff, 0, delta=1E-14)
def test_constant_solution(): """compare to the constant solution u = 1.2""" Lx = 10 Ly = 10 def c(x,y): s = (np.size(x),np.size(y)) c = np.zeros(s) c = c + 1 return c def I(x, y): """constant solution u = 1.2, should be exact""" return 1.2 Nx = 40; Ny = 40; T = 20 u_exact = 1.2*np.ones((Nx+1,Ny+1)) for version in ['scalar','vectorized']: dt,time, T2 = bw.solver(I, None, None, c, 0.0, Lx, Ly, Nx, Ny, 0.1, T, version=version) n = int(T/dt - 1) fname = 'solution_%06d.txt' % n u = np.loadtxt(fname) diff = np.abs(u_exact - u).max() nt.assert_almost_equal(diff, 0, delta=1E-14)
def test_quadratic():
"""test for convergence rate in manufactured solution"""
Lx = 4.
Ly = 4.
def c(x, y):
s = (np.size(x), np.size(y))
c = np.zeros(s)
c = c + 1
return c
mx = 4.
my = 4.
b = 0.01
omega = np.pi
def u_exact(x, y, t):
return np.exp(-b * t) * np.cos(mx * x * np.pi / Lx) * np.cos(
my * y * np.pi / Ly) * np.cos(omega * t)
def f(x, y, t):
return np.exp(-b*t)*np.cos(mx*np.pi*x/Lx)*np.cos(my*np.pi*y/Ly)*(b*omega*np.sin(omega*t) + \
( - omega*omega + (mx*np.pi/Lx)**2 + (my*np.pi/Ly)**2 )*np.cos(omega*t))
def I(x, y):
return np.cos(mx * np.pi * x / Lx) * np.cos(my * np.pi * y / Ly)
def V(x, y):
return -b * np.cos(mx * np.pi * x / Lx) * np.cos(my * np.pi * y / Ly)
Nx = 40
Ny = 40
T = 1.0
dt = 0.01
fac = 1.
for version in ['scalar', 'vectorized']:
errorlist = [0, 0, 0, 0]
for i in range(3):
x = np.linspace(0, Lx, Nx + 1)
dx = x[1] - x[0] # mesh points in x dir
y = np.linspace(0, Ly, Ny + 1)
dy = y[1] - y[0] # mesh points in y dir
dt, time, T2 = bw.solver(I,
V,
f,
c,
b,
Lx,
Ly,
Nx,
Ny,
dt,
T,
version=version)
n = int(T / dt)
fname = 'solution_%06d.txt' % n
u = np.loadtxt(fname)
X, Y = np.meshgrid(x, y)
u_ex = u_exact(X, Y, T2)
error = np.copy((u_ex - u)**2)
error = np.sum(error)
error = np.sqrt(error * dx * dy)
errorlist[i] = error
Nx = Nx * 2
Ny = Ny * 2
dt = dt / 2
ratio1 = errorlist[1] / errorlist[0]
ratio2 = errorlist[2] / errorlist[1]
nt.assert_almost_equal(ratio1, 0.25, delta=0.06)
nt.assert_almost_equal(ratio2, 0.25, delta=0.06)