Fipy中对流系数的控制：对流扩散方程

Question

我试图用fipy在python中求解对流扩散方程。我想操纵对流系数，使它指向区域的中心。在

我的代码是

from fipy import *

# Setting mesh and discretising space
nx = 10
dx = 1.
mesh = Grid1D(nx=nx, dx=dx)
x = mesh.cellCenters[0]

# Setting variable of results and adding inicial conditions
phi = CellVariable(name="solution variable", mesh=mesh, value=0.)
phi.setValue(1., where=(4 < x) & (6 > x))

# Plotting inicial conditions
if __name__ == '__main__':
    viewer = Viewer(vars=phi, datamin=-0.1, datamax=1.5)
    viewer.plot()

# Diffusion and convection coefficients
D = 1.
C = (1.,)

# Setting PDE
eqX = TransientTerm() == DiffusionTerm(coeff=D) - \
                     ConvectionTerm(coeff=C)

# Solving Transient term
timeStepDuration = 0.1
steps = 15
t = timeStepDuration * steps

for step in range(steps):
eqX.solve(var=phi, dt=timeStepDuration)

# Plotting results
if __name__ == '__main__':
    viewer = Viewer(vars=phi, datamin=0., datamax=1.)
    viewer.plot()

正如你所看到的，随着时间的推移，波沿着对流系数向量确定的方向移动。当波只朝我的区域中心移动时，如何操纵对流系数呢？在

任何建议都将不胜感激！在

Answer 1

对流系数控制着行波的方向。例如，为了使波始终向区域中心移动，将对流系数改为

C = CellVariable(mesh=mesh, rank=1)
C[:] = 1.
C.setValue(-1., where=x > 5.)

如果波在域的前半部分，它将使波以速度1平流；如果波在域的后半部分，则速度为-1。如果初始方波偏离中心，那么它将返回中心。在