#for scheme in ['CDS', 'UDS', 'ES', 'HS', 'PS']:
print(vC.shape)
neumannBC = [[5, 0]]
Peclet = 5000 # vel/diffus
scheme='UDS'
dirichletBC = [[1, lambda b_: 1. - np.tanh(10.)],
[2, lambda b_: 1. - np.tanh(10.)],
[3, lambda b_: 1. - np.tanh(10.)],
[4, lambda b_: 1. + np.tanh(10 * (2 * b_.center()[0] + 1.))],
]
print ("start", swatch.duration())
uGrid = solveFiniteVolume(grid, a=1./Peclet, f=f, vel=vB,
uBoundary=dirichletBC,
duBoundary=neumannBC,
scheme=scheme)
pg.showLater(1)
ax1,cb = show(grid)
drawStreams(ax1, grid, vC, coarseMesh=pg.createGrid(x=np.linspace(-1.0, 1.0, 41),
y=np.linspace(0.0, 1.0, 21)),
)
print(swatch.duration())
#grid2, u2 = createFVPostProzessMesh(grid, u, dirichletBC)
show(grid, data=uGrid,
logScale=False, interpolate=1, tri=1,
k = 0.1
uFE = solver.solveFiniteElements(grid, a=a, b=k*k, f=pointSource,
duBoundary=neumannBC,
uBoundary=dirichletBC,
userData={'sourcePos': sourcePosA, 'k': k},
verbose=True)
pg.showLater(1)
ax1, cb = show(grid, uFE,
cMin=0, cMax=1, nLevs=10, colorBar=True)
drawMesh(ax1, grid)
f = pg.Vector(grid.cellCount(), 0)
f[grid.findCell(sourcePosA).id()]=1.0/grid.findCell(sourcePosA).size()
uFV = solveFiniteVolume(grid, a=a, b=k*k, f=f,
duBoundary=neumannBC,
uBoundary=dirichletBC,
userData={'sourcePos': sourcePosA, 'k': k},
verbose=True)
#print('FVM:', swatch.duration(True))
ax2, cb = show(grid, uFV, interpolate=1, tri=1,
cMin=0, cMax=1, nLevs=10, colorBar=True)
drawMesh(ax2, grid)
pg.showNow()
ud0=0
udN=1
def uAna(x, L, v, D):
"""
u = \frac{1 - \e(-v_x x / D)}{1 - \e(-v_x L / D)}
Check for -v -- herleiten
"""
return (1 - np.exp(v * x / D))/(1. - np.exp(v * L / D))
plt.plot(np.linspace(0,1,100),
uAna(np.linspace(0,1,100), L=1.0, v=v[0], D=a[1]),
'-', label='exact')
for scheme in ['CDS', 'UDS', 'ES', 'HS', 'PS']:
S, rhs = diffusionConvectionKernelGrid(grid, a, f, v, uDir=[ud0, udN], scheme=scheme)
u = np.linalg.solve(S, rhs)
plt.plot(pg.x(grid.cellCenter()), u[1:N+1], 'o-', label='FVM-'+scheme)
vC = np.vstack((v,np.zeros(len(v)))).T
uFV = solveFiniteVolume(grid, a=a, f=f, vel=vC,
uBoundary=[[1,ud0],[2,udN]], scheme='HS')
plt.plot(pg.x(grid.cellCenter()), uFV, 'o-', label='FVM-2 (mesh)')
plt.legend()
plt.show()
#drawMesh(ax, grid)
#for scheme in ['CDS', 'UDS', 'ES', 'HS', 'PS']:
print(vC.shape)
neumannBC = [[5, 0]]
Peclet = 500 # vel/diffus
scheme='UDS'
dirichletBC = [[1, lambda b_: 1. - np.tanh(10.)],
[2, lambda b_: 1. - np.tanh(10.)],
[3, lambda b_: 1. - np.tanh(10.)],
[4, lambda b_: 1. + np.tanh(10 * (2 * b_.center()[0] + 1.))],
]
print ("start", swatch.duration())
uGrid = solveFiniteVolume(grid, a=1./Peclet, f=f, vel=vB,
uBoundary=dirichletBC,
duBoundary=neumannBC,
scheme=scheme)
ax1,cb = show(grid)
drawStreams(ax1, grid, vC, coarseMesh=pg.createGrid(x=np.linspace(-1.0, 1.0, 41),
y=np.linspace(0.0, 1.0, 21)),
)
print(swatch.duration())
#grid2, u2 = createFVPostProzessMesh(grid, u, dirichletBC)
show(grid, data=uGrid,
logScale=False, interpolate=1, tri=1,
colorBar=True, axes=ax1)
ud0 = 0
udN = 1
def uAna(x, L, v, D):
"""
u = \frac{1 - \e(-v_x x / D)}{1 - \e(-v_x L / D)}
Check for -v -- herleiten
"""
return (1 - np.exp(v * x / D)) / (1.0 - np.exp(v * L / D))
plt.plot(np.linspace(0, 1, 100), uAna(np.linspace(0, 1, 100), L=1.0, v=v[0], D=a[1]), "-", label="exact")
for scheme in ["CDS", "UDS", "ES", "HS", "PS"]:
S, rhs = diffusionConvectionKernelGrid(grid, a, f, v, uDir=[ud0, udN], scheme=scheme)
u = np.linalg.solve(S, rhs)
plt.plot(pg.x(grid.cellCenter()), u[1 : N + 1], "o-", label="FVM-" + scheme)
vC = np.vstack((v, np.zeros(len(v)))).T
uFV = solveFiniteVolume(grid, a=a, f=f, vel=vC, uBoundary=[[1, ud0], [2, udN]], scheme="HS")
plt.plot(pg.x(grid.cellCenter()), uFV, "o-", label="FVM-2 (mesh)")
plt.legend()
plt.show()
# drawMesh(ax, grid)
showLater=True)
drawMesh(ax1, mesh)
#print(min(u), max(u))
uAna = np.array(list(map(lambda p_: np.sin(np.arctan2(p_[1],
p_[0]))/p_.abs(),
mesh.positions())))
#drawStreamLines2(ax1, mesh, data=u)
#ax2,cbar = showMesh(mesh, data=(u+1e-6)/(ua+1e-6), filled=True, colorBar=True, showLater=True)
#showMesh(amesh)
print('---:', swatch.duration(True))
uFV = solveFiniteVolume(mesh, a=a, f=f, uBoundary=uDirichlet)
print('FVM:', swatch.duration(True))
ax2, cbar = showMesh(mesh,
data=uFV,
cMin=0, cMax=10, logScale=False,
interpolate=False, shading='gouraud',
tri=1,
nLevs=12,
colorBar=True, showLater=True)
drawMesh(ax2, mesh)
#allBounds = pg.solver.parseArgToBoundaries(uDirichlet, mesh)
#bounds, vals = zip(*allBounds)
#uDirVals = pg.solver.generateBoundaryValue(bounds, vals)
showLater=True)
drawMesh(ax1, mesh)
#print(min(u), max(u))
uAna = np.array(
list(
map(lambda p_: np.sin(np.arctan2(p_[1], p_[0])) / p_.abs(),
mesh.positions())))
#drawStreamLines2(ax1, mesh, data=u)
#ax2,cbar = showMesh(mesh, data=(u+1e-6)/(ua+1e-6), filled=True, colorBar=True, showLater=True)
#showMesh(amesh)
print('---:', swatch.duration(True))
uFV = solveFiniteVolume(mesh, a=a, f=f, uBoundary=uDirichlet)
print('FVM:', swatch.duration(True))
ax2, cbar = showMesh(mesh,
data=uFV,
cMin=0,
cMax=10,
logScale=False,
interpolate=False,
shading='gouraud',
tri=1,
nLevs=12,
colorBar=True,
showLater=True)
drawMesh(ax2, mesh)
solver.assembleBoundaryConditions(grid, S,
rhs=rhs,
boundArgs=dirichletBC,
assembler=solver.assembleDirichletBC)
uFEM[n] = solver.linsolve(S, rhs)
#ax1.plot(x, uE[timeProbeID], label='FD explicit')
#ax2.plot(t, uE[:,spaceProbeID], label='FD explicit')
ax1.plot(x, uI[timeProbeID], '.-', label='FD implicit')
ax2.plot(t, uI[:, spaceProbeID], '.-', label='FD implicit')
#ax1.plot(x, uFEM[timeProbeID], label='FE implicit')
#ax2.plot(t, uFEM[:,spaceProbeID], label='FE implicit')
uFVM = solveFiniteVolume(grid, a=tempLF, f=0.0, times=t, u0=u0,
uDirichlet=[0.0, 0.0])
print(len(uFVM), len(uFVM[0]))
ax1.plot(pg.x(grid.cellCenters()), uFVM[timeProbeID], '.-',
label='FV implicit')
ax2.plot(t, uFVM[:, spaceProbeID], '.-', label='FV implicit')
uFE = solver.solvePoisson(grid, times=t, a=tempLF, theta=0.5, u0=u0,
uBoundary=dirichletBC)
ax1.plot(x, uFE[timeProbeID], label='FE Crank-Nicolsen')
ax2.plot(t, uFE[:, spaceProbeID], label='FE Crank-Nicolsen')
ax1.legend()
ax2.legend()
k = 0.1
uFE = solver.solveFiniteElements(grid, a=a, b=k*k, f=pointSource,
duBoundary=neumannBC,
uBoundary=dirichletBC,
userData={'sourcePos': sourcePosA, 'k': k},
verbose=True)
pg.showLater(1)
ax1, cb = show(grid, uFE,
cMin=0, cMax=1, nLevs=10, colorBar=True)
drawMesh(ax1, grid)
f = pg.RVector(grid.cellCount(), 0)
f[grid.findCell(sourcePosA).id()]=1.0/grid.findCell(sourcePosA).size()
uFV = solveFiniteVolume(grid, a=a, b=k*k, f=f,
duBoundary=neumannBC,
uBoundary=dirichletBC,
userData={'sourcePos': sourcePosA, 'k': k},
verbose=True)
#print('FVM:', swatch.duration(True))
ax2, cb = show(grid, uFV, interpolate=1, tri=1,
cMin=0, cMax=1, nLevs=10, colorBar=True)
drawMesh(ax2, grid)
pg.showNow()
