Python 调整FiPy'；1D场景的s Flow.stokesCavity示例

正如所建议的，我已经用FiPy中的Stokes空腔例子攻击了我的一维可压缩流（我真的想用FiPy来描述那个模型）。但它仍然不起作用。在扫描过程中，我得到错误“对于秩0的解决方案变量，系数必须为秩0”。我非常了解如何解决这个问题，但也理解为什么会出现这个错误

使用的代码：

from fipy import CellVariable, FaceVariable, Grid1D, DiffusionTerm, Viewer
from fipy.tools import numerix
import matplotlib.pyplot as plt

L = 1.0
N = 50
dL = L / N
viscosity = 1
#0.8 for pressure and 0.5 for velocity are typical relaxation values for SIMPLE
pressureRelaxation = 0.8
velocityRelaxation = 0.5
if __name__ == '__main__':
    sweeps = 300
else:
    sweeps = 5

mesh = Grid1D(nx=N, dx=dL)  

pressure = CellVariable(mesh=mesh, name='pressure')
pressureCorrection = CellVariable(mesh=mesh)
xVelocity = CellVariable(mesh=mesh, name='X velocity')

velocity = FaceVariable(mesh=mesh, rank = 1)
xVelocityEq = DiffusionTerm(coeff=viscosity) - pressure.grad.dot([1.])

ap = CellVariable(mesh=mesh, value=1.)
coeff = 1./ ap.arithmeticFaceValue*mesh._faceAreas * mesh._cellDistances
pressureCorrectionEq = DiffusionTerm(coeff=coeff) - velocity.divergence

from fipy.variables.faceGradVariable import _FaceGradVariable
volume = CellVariable(mesh=mesh, value=mesh.cellVolumes, name='Volume')
contrvolume=volume.arithmeticFaceValue

xVelocity.constrain(10., mesh.facesRight | mesh.facesLeft )
X = mesh.faceCenters
pressureCorrection.constrain(0., mesh.facesLeft)

from builtins import range
for sweep in range(sweeps):

    ## solve the Stokes equations to get starred values
    xVelocityEq.cacheMatrix()
    xres = xVelocityEq.sweep(var=xVelocity,
                             underRelaxation=velocityRelaxation)
    xmat = xVelocityEq.matrix

    ## update the ap coefficient from the matrix diagonal
    ap[:] = -numerix.asarray(xmat.takeDiagonal())

    ## update the face velocities based on starred values with the
    ## Rhie-Chow correction.
    ## cell pressure gradient
    presgrad = pressure.grad
    ## face pressure gradient
    facepresgrad = _FaceGradVariable(pressure)

    velocity[0] = xVelocity.arithmeticFaceValue \
         + contrvolume / ap.arithmeticFaceValue * \
           (presgrad[0].arithmeticFaceValue-facepresgrad[0])
    velocity[..., mesh.exteriorFaces.value] = 0.

    ## solve the pressure correction equation
    pressureCorrectionEq.cacheRHSvector()
    ## left bottom point must remain at pressure 0, so no correction
    pres = pressureCorrectionEq.sweep(var=pressureCorrection)
    rhs = pressureCorrectionEq.RHSvector

    ## update the pressure using the corrected value
    pressure.setValue(pressure + pressureRelaxation * pressureCorrection )
    ## update the velocity using the corrected pressure
    xVelocity.setValue(xVelocity - pressureCorrection.grad[0] / \
                                               ap * mesh.cellVolumes)

    if __name__ == '__main__':
        if sweep%10 == 0:
            print('sweep:', sweep, ', x residual:', xres, \
                                 ', p residual:', pres, \
                                 ', continuity:', max(abs(rhs)))

            viewer.plot()

---

这是一件微妙的事情，但菲比没有把单位向量识别为向量。尝试：

xVelocityEq=扩散项（系数=粘度）-压力梯度点（[[1.]]