如何将零通量边界条件添加到 gmsh Fipy 中生成的网格？

Question

我正在尝试在由 gmsh 在 Fipy 中创建的网格中求解 Meinhart 模型。但是，我不确定如何添加零通量边界条件。在下面，您可以找到我的代码。我想知道是否有以下几行：

#u.constrain(0, where=mesh.exteriorFaces)
#u.faceGrad.constrain(mesh.faceCenters, where=mesh.exteriorFaces)

应激活以确保零通量边界条件。

我读入：https://github.com/usnistgov/fipy/issues/674 "FiPy's boundaries are no-flux by default"。但是，我不知道它是否也适用于 gmsh 选项创建的网格。

如果不需要激活或在我的代码中添加额外的行来设置零通量边界条件，它也适用于我有更复杂的网格，例如多边形、圆形或其他不规则形状？

谢谢，

"""
Emacs Editor

This is a temporary script file.
"""

# -*- coding: utf-8 -*-
"""
@author: Irbin B.
"""
'''Solving Meinhart model 2D'''


# 1. Libraries
import fipy as fi                   # Finite volume method's package

# 2. Building the domain (Gmsh square)
## 2.1. Domain lenght
nx = 100
ny = nx

## 2.2. Gmsh config
mesh = fi.Gmsh2D('''
Side = 100;
CellSize = 1;
Point(1) = {0, 0, 0, CellSize};   
Point(2) = {0, Side, 0, CellSize};
Point(3) = {Side, Side, 0, CellSize};
Point(4) = {Side, 0, 0, CellSize};
Line(1) = {1, 2};
Line(2) = {2, 3};
Line(3) = {3, 4};
Line(4) = {4, 1};
Line Loop(6) = {1, 2, 3, 4};
Plane Surface(7) = {6};
''' % locals())


## 2.3. Adding initial conditions values (Random)
noise_u = fi.GaussianNoiseVariable(mesh=mesh,
                                   mean=0.5,
                                   variance=0.05).value
noise_v = fi.GaussianNoiseVariable(mesh=mesh,
                                   mean=0.5,
                                   variance=0.05).value

# 3. Zero-Flux boundary conditions
BCs = (fi.FixedFlux(faces=mesh.facesRight, value=0.),
       fi.FixedFlux(faces=mesh.facesLeft, value=0.),
       fi.FixedFlux(faces=mesh.facesTop, value=0.),
       fi.FixedFlux(faces=mesh.facesBottom, value=0.))

# 4. Defining the variables
u = fi.CellVariable(name = "u",
                    mesh=mesh,
                    value=0.,
                    hasOld=True)

u[:] = noise_u
#u.constrain(0, where=mesh.exteriorFaces)
#u.faceGrad.constrain(mesh.faceCenters, where=mesh.exteriorFaces)

v = fi.CellVariable(name = "v",
                    mesh = mesh,
                    value = 0.,
                    hasOld = True)

v[:] = noise_v
#v.constrain(0, where=mesh.exteriorFaces)
#v.faceGrad.constrain(mesh.faceCenters, where=mesh.exteriorFaces)

# 5. Defining the parameters
Da = 1.
Db = 100
alpha = -0.005
beta = 10

# 6. Creating the system of PDEs
equ = fi.TransientTerm(var=u) == fi.DiffusionTerm(coeff=Da, var=u) + u - u**3 - v + alpha

eqv = fi.TransientTerm(var=v) == fi.DiffusionTerm(coeff=Db, var=v) + (u - v) * beta

eqn = (equ & eqv)

# 7. Solving the PDEs and showing the results in figures
timeStepDuration = .1
steps = 100


for step in range(steps):
    u.updateOld()
    v.updateOld()
    eqn.sweep(dt = timeStepDuration)
    print(step+1)

if __name__== '__main__':
    uviewer = fi.Viewer(vars=u, datamin=0., datamax=.7)
    vviewer = fi.Viewer(vars=v, datamin=0., datamax=.7)

Answer 1

FiPy 的边界条件对于所有网格默认都是无通量的。这是以单元为中心的有限体积法的一个基本特征。

如何将零通量边界条件添加到 gmsh Fipy 中生成的网格？

How to add zero-flux boundary conditions to a mesh generated in gmsh Fipy?

python

pde

fipy