关于多相流的电势方程（Laplace方程）的求解问题

李东岳

你求解的方程没有时间项不需要时间步进，你运行一个时间步就行。如果你的电场力和速度、压力耦合，那需要贴更多的代码和方程

你可以先debug一下你的fvm::laplacian( sigmaE, phiE)求解的结果正确与否，再双向耦合

cfd_lilili

@东岳

谢谢东岳老师！

我简单修改了一下代码，让它迭代多次

    scalar phiEEqRes = cttProperties.lookupOrDefault<scalar>("phiEEqRes", 1e-6 ) ;

    // Max number of iterations
    int maxIterPhiE = cttProperties.lookupOrDefault<int>("maxIterPhiE", 20 ) ;

   // Transport of passive scalar

    sigmaE == alpha1*sigmaE1 + alpha2*sigmaE2;

    scalar res=GREAT;
    int    iter=0;  

    while (res > phiEEqRes && iter < maxIterPhiE)
    {

        fvScalarMatrix phiEEqn
        (
            fvm::laplacian( sigmaE, phiE) 
        );

        phiEEqn.relax();
        res = phiEEqn.solve().initialResidual();

        iter++;

    }

同样的算例下，log文件如下

/*---------------------------------------------------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  4.x                                   |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
Build  : 4.x
Exec   : rheoEHDPhaseFieldFoam
Date   : Oct 28 2019
Time   : 11:01:00
Host   : "cfd"
PID    : 103447
Case   : /home/cfd/OpenFOAM/cfd-4.x/run/rheoEHDPhaseFieldFoam/electric_test2
nProcs : 1
sigFpe : Enabling floating point exception trapping (FOAM_SIGFPE).
fileModificationChecking : Monitoring run-time modified files using timeStampMaster
allowSystemOperations : Allowing user-supplied system call operations

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
Create time

Create mesh for time = 0


PIMPLE: Operating solver in PISO mode

Reading field p_rgh

Reading field U

Reading/calculating face flux field phi

Reading transportProperties

Selecting constitutive equation Newtonian
Selecting constitutive equation Newtonian

Reading g

Reading hRef
Calculating field g.h

No MRF models present

No finite volume options present

DICPCG:  Solving for pcorr, Initial residual = 0, Final residual = 0, No Iterations 0
time step continuity errors : sum local = 0, global = 0, cumulative = 0
Courant Number mean: 0 max: 0

Starting time loop

Courant Number mean: 0 max: 0
Interface Courant Number mean: 0 max: 0
Time = 0.001

Phase-1 volume fraction = 0.0248178  Min(alpha.water) = -2.12354e-55  Max(alpha.water) - 1 = 0
smoothSolver:  Solving for phiE, Initial residual = 2.00047e-06, Final residual = 9.0829e-09, No Iterations 2
smoothSolver:  Solving for phiE, Initial residual = 2.00062e-06, Final residual = 9.08496e-09, No Iterations 2
smoothSolver:  Solving for phiE, Initial residual = 2.00079e-06, Final residual = 9.08756e-09, No Iterations 2
smoothSolver:  Solving for phiE, Initial residual = 2.00098e-06, Final residual = 9.09235e-09, No Iterations 2
smoothSolver:  Solving for phiE, Initial residual = 2.00131e-06, Final residual = 9.10815e-09, No Iterations 2
smoothSolver:  Solving for phiE, Initial residual = 2.0024e-06, Final residual = 9.20389e-09, No Iterations 2
smoothSolver:  Solving for phiE, Initial residual = 2.00751e-06, Final residual = 1.05039e-08, No Iterations 2
smoothSolver:  Solving for phiE, Initial residual = 2.06764e-06, Final residual = 2.18651e-08, No Iterations 2
smoothSolver:  Solving for phiE, Initial residual = 2.72883e-06, Final residual = 8.38954e-08, No Iterations 2
smoothSolver:  Solving for phiE, Initial residual = 7.30545e-06, Final residual = 2.6689e-08, No Iterations 4
smoothSolver:  Solving for phiE, Initial residual = 3.10926e-05, Final residual = 3.82843e-08, No Iterations 5
smoothSolver:  Solving for phiE, Initial residual = 0.000149551, Final residual = 5.68219e-08, No Iterations 6
smoothSolver:  Solving for phiE, Initial residual = 0.000753353, Final residual = 8.61768e-08, No Iterations 7
smoothSolver:  Solving for phiE, Initial residual = 0.00389063, Final residual = 3.72685e-08, No Iterations 9
smoothSolver:  Solving for phiE, Initial residual = 0.0201471, Final residual = 5.71e-08, No Iterations 10
smoothSolver:  Solving for phiE, Initial residual = 0.0968377, Final residual = 8.0832e-08, No Iterations 11
smoothSolver:  Solving for phiE, Initial residual = 0.330082, Final residual = 8.08282e-08, No Iterations 12
smoothSolver:  Solving for phiE, Initial residual = 0.583957, Final residual = 4.1842e-08, No Iterations 13
smoothSolver:  Solving for phiE, Initial residual = 0.671177, Final residual = 4.92793e-08, No Iterations 13
smoothSolver:  Solving for phiE, Initial residual = 0.687466, Final residual = 5.15537e-08, No Iterations 13
DILUPBiCG:  Solving for Ux, Initial residual = 1, Final residual = 8.88689e-11, No Iterations 49
DILUPBiCG:  Solving for Uy, Initial residual = 1, Final residual = 8.54483e-11, No Iterations 47
DILUPBiCG:  Solving for Uz, Initial residual = 1, Final residual = 9.77718e-11, No Iterations 46
DICPCG:  Solving for p_rgh, Initial residual = 1, Final residual = 9.26224e-11, No Iterations 481
time step continuity errors : sum local = 5.4911e-05, global = -9.71439e-09, cumulative = -9.71439e-09
ExecutionTime = 9.1 s  ClockTime = 9 s

Courant Number mean: 1.63727e+07 max: 5.36038e+08
Interface Courant Number mean: 1.56047e+06 max: 5.36038e+08
Time = 0.002

#0  Foam::error::printStack(Foam::Ostream&) at ??:?
#1  Foam::sigFpe::sigHandler(int) at ??:?
#2  ? in "/lib/x86_64-linux-gnu/libc.so.6"
#3  Foam::multiply(Foam::Field<double>&, Foam::UList<double> const&, Foam::UList<double> const&) at ??:?
#4  Foam::tmp<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh> > Foam::operator*<Foam::fvPatchField, Foam::volMesh>(Foam::tmp<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh> > const&, Foam::tmp<Foam::GeometricField<double, Foam::fvPatchField, Foam::volMesh> > const&) at ??:?
#5  Foam::interfaceEHDPropertiesPFM::calculateMobility() at ??:?
#6  ? at ??:?
#7  ? at ??:?
#8  __libc_start_main in "/lib/x86_64-linux-gnu/libc.so.6"
#9  ? at ??:?

可以看到，Initial residual在几个迭代步后迅速增大，这应该是计算发散的表征。这个算例里，我的不同相的sigmaE的比值是5，Laplace方程求解的格式是常用的Gauss linear corrected。所以，我猜想这应该和我引入的电场力无关，而主要是laplace方程的求解分散问题。

李东岳

@cfd_lilili 在关于多相流的电势方程（Laplace方程）的求解问题中说：

fvScalarMatrix phiEEqn
(
fvm::laplacian( sigmaE, phiE)
);

这个方程不需要迭代多次

yfclark

这个应该是类似虚假流动的现象，初始化的时候给个电场和压力梯度表面张力平衡的的初始场试一下会不会好一点

cfd_lilili

@东岳和@yfclark 感谢两位的建议
对这个问题，我实在无从下手，于是刚刚尝试了一下换个版本的求解器试试看。于是，我将同样的代码片段植入到of4.0和fe4.0的interFoam求解器中，并做了同样的算例。结果发现同样的条件下的Laplace方程，of4.0解不了，fe4.0可以解。这让我很迷惑。

这个是of4.0求解器的算例的log文件，可以看到它的 Initial residual并没有收敛的迹象。

/*---------------------------------------------------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  4.x                                   |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
Build  : 4.x
Exec   : interFoamtest
Date   : Oct 28 2019
Time   : 16:51:11
Host   : "cfd"
PID    : 116917
Case   : /home/cfd/OpenFOAM/cfd-4.x/run/interFoamtest/damBreak
nProcs : 1
sigFpe : Enabling floating point exception trapping (FOAM_SIGFPE).
fileModificationChecking : Monitoring run-time modified files using timeStampMaster
allowSystemOperations : Allowing user-supplied system call operations

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
Create time

Create mesh for time = 0


PIMPLE: Operating solver in PISO mode

Reading field p_rgh

Reading field U

Reading/calculating face flux field phi

Reading transportProperties

Selecting incompressible transport model Newtonian
Selecting incompressible transport model Newtonian
Selecting turbulence model type laminar

Reading g

Reading hRef
Calculating field g.h

No MRF models present

No finite volume options present

DICPCG:  Solving for pcorr, Initial residual = 0, Final residual = 0, No Iterations 0
time step continuity errors : sum local = 0, global = 0, cumulative = 0
Courant Number mean: 0 max: 0

Starting time loop

Courant Number mean: 0 max: 0
Interface Courant Number mean: 0 max: 0
Time = 0.001

PIMPLE: iteration 1
smoothSolver:  Solving for alpha.water, Initial residual = 0, Final residual = 0, No Iterations 0
Phase-1 volume fraction = 0.0247173  Min(alpha.water) = 0  Max(alpha.water) = 1
MULES: Correcting alpha.water
MULES: Correcting alpha.water
Phase-1 volume fraction = 0.0247173  Min(alpha.water) = 0  Max(alpha.water) = 1
smoothSolver:  Solving for phiE, Initial residual = 1, Final residual = 0.00666667, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.969654, Final residual = 0.955898, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999906, Final residual = 0.999906, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999943, Final residual = 0.999943, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999959, Final residual = 0.999959, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.99997, Final residual = 0.99997, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999977, Final residual = 0.999977, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999982, Final residual = 0.999982, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999986, Final residual = 0.999986, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999989, Final residual = 0.999989, No Iterations 1000
DICPCG:  Solving for p_rgh, Initial residual = 1, Final residual = 0.0288118, No Iterations 2
time step continuity errors : sum local = 3.79873e-07, global = -1.14217e-22, cumulative = -1.14217e-22
DICPCG:  Solving for p_rgh, Initial residual = 0.014257, Final residual = 0.000679011, No Iterations 51
time step continuity errors : sum local = 1.80931e-08, global = 1.97801e-23, cumulative = -9.44368e-23
DICPCG:  Solving for p_rgh, Initial residual = 0.000685827, Final residual = 9.85239e-08, No Iterations 330
time step continuity errors : sum local = 2.59978e-12, global = -2.24454e-24, cumulative = -9.66814e-23
ExecutionTime = 29.16 s  ClockTime = 29 s

Courant Number mean: 8.45892e-06 max: 0.00486238
Interface Courant Number mean: 0 max: 0
Time = 0.002

PIMPLE: iteration 1
smoothSolver:  Solving for alpha.water, Initial residual = 1.03138e-05, Final residual = 1.278e-11, No Iterations 1
Phase-1 volume fraction = 0.0247173  Min(alpha.water) = 0  Max(alpha.water) = 1
MULES: Correcting alpha.water
MULES: Correcting alpha.water
Phase-1 volume fraction = 0.0247173  Min(alpha.water) = -1.02138e-12  Max(alpha.water) = 1
smoothSolver:  Solving for phiE, Initial residual = 0.999991, Final residual = 0.999991, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999993, Final residual = 0.999993, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999994, Final residual = 0.999994, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999995, Final residual = 0.999995, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999996, Final residual = 0.999996, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999997, Final residual = 0.999997, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999997, Final residual = 0.999997, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999998, Final residual = 0.999998, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999998, Final residual = 0.999998, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999998, Final residual = 0.999998, No Iterations 1000
DICPCG:  Solving for p_rgh, Initial residual = 0.148216, Final residual = 0.00717185, No Iterations 8
time step continuity errors : sum local = 1.53736e-07, global = 1.00047e-22, cumulative = 3.36563e-24
DICPCG:  Solving for p_rgh, Initial residual = 0.00694699, Final residual = 0.00032885, No Iterations 69
time step continuity errors : sum local = 7.31529e-09, global = -5.63383e-24, cumulative = -2.2682e-24
DICPCG:  Solving for p_rgh, Initial residual = 0.000331229, Final residual = 9.04502e-08, No Iterations 320
time step continuity errors : sum local = 2.00174e-12, global = -1.03358e-23, cumulative = -1.2604e-23
ExecutionTime = 55.26 s  ClockTime = 55 s

Courant Number mean: 1.00744e-05 max: 0.00608536
Interface Courant Number mean: 0 max: 0
Time = 0.003

PIMPLE: iteration 1
smoothSolver:  Solving for alpha.water, Initial residual = 1.17667e-05, Final residual = 1.48862e-11, No Iterations 1
Phase-1 volume fraction = 0.0247173  Min(alpha.water) = -7.81203e-23  Max(alpha.water) = 1
MULES: Correcting alpha.water
MULES: Correcting alpha.water
Phase-1 volume fraction = 0.0247173  Min(alpha.water) = -2.49888e-15  Max(alpha.water) = 1
smoothSolver:  Solving for phiE, Initial residual = 0.999998, Final residual = 0.999998, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
DICPCG:  Solving for p_rgh, Initial residual = 0.0570031, Final residual = 0.00216312, No Iterations 3
time step continuity errors : sum local = 4.53781e-08, global = -1.07358e-25, cumulative = -1.27114e-23
DICPCG:  Solving for p_rgh, Initial residual = 0.00216994, Final residual = 0.000103227, No Iterations 32
time step continuity errors : sum local = 2.19448e-09, global = 2.56894e-23, cumulative = 1.29781e-23
DICPCG:  Solving for p_rgh, Initial residual = 0.000103679, Final residual = 9.68435e-08, No Iterations 180
time step continuity errors : sum local = 2.06555e-12, global = 2.39499e-23, cumulative = 3.6928e-23
ExecutionTime = 80.51 s  ClockTime = 80 s

Courant Number mean: 1.02305e-05 max: 0.0059902
Interface Courant Number mean: 0 max: 0
Time = 0.004

PIMPLE: iteration 1
smoothSolver:  Solving for alpha.water, Initial residual = 1.14624e-05, Final residual = 1.20817e-11, No Iterations 1
Phase-1 volume fraction = 0.0247173  Min(alpha.water) = -2.32959e-16  Max(alpha.water) = 1
MULES: Correcting alpha.water
MULES: Correcting alpha.water
Phase-1 volume fraction = 0.0247173  Min(alpha.water) = -6.27415e-12  Max(alpha.water) = 1
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
DICPCG:  Solving for p_rgh, Initial residual = 0.025679, Final residual = 0.00121229, No Iterations 2
time step continuity errors : sum local = 2.4847e-08, global = 4.56559e-24, cumulative = 4.14936e-23
DICPCG:  Solving for p_rgh, Initial residual = 0.00123628, Final residual = 5.7827e-05, No Iterations 29
time step continuity errors : sum local = 1.18735e-09, global = -1.92179e-25, cumulative = 4.13014e-23
DICPCG:  Solving for p_rgh, Initial residual = 5.83662e-05, Final residual = 9.44483e-08, No Iterations 129
time step continuity errors : sum local = 1.94768e-12, global = -2.79384e-23, cumulative = 1.3363e-23
ExecutionTime = 105.48 s  ClockTime = 105 s

Courant Number mean: 1.02721e-05 max: 0.00571222
Interface Courant Number mean: 0 max: 0
Time = 0.005

PIMPLE: iteration 1
smoothSolver:  Solving for alpha.water, Initial residual = 1.10272e-05, Final residual = 9.91906e-12, No Iterations 1
Phase-1 volume fraction = 0.0247173  Min(alpha.water) = -1.84397e-16  Max(alpha.water) = 1
MULES: Correcting alpha.water
MULES: Correcting alpha.water
Phase-1 volume fraction = 0.0247173  Min(alpha.water) = -5.64491e-12  Max(alpha.water) = 1
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.999999, Final residual = 0.999999, No Iterations 1000
DICPCG:  Solving for p_rgh, Initial residual = 0.0170557, Final residual = 0.000707649, No Iterations 2
time step continuity errors : sum local = 1.40556e-08, global = 5.55595e-24, cumulative = 1.8919e-23
DICPCG:  Solving for p_rgh, Initial residual = 0.00072258, Final residual = 3.40642e-05, No Iterations 66
time step continuity errors : sum local = 6.7235e-10, global = -1.97122e-24, cumulative = 1.69477e-23
DICPCG:  Solving for p_rgh, Initial residual = 3.47482e-05, Final residual = 9.44334e-08, No Iterations 110
time step continuity errors : sum local = 1.97407e-12, global = 2.71579e-25, cumulative = 1.72193e-23
ExecutionTime = 132.15 s  ClockTime = 132 s

Courant Number mean: 1.03787e-05 max: 0.00551763

这里是fe4.0的求解器的算例的log文件，它的Initial residual则呈现了收敛的趋势

/*---------------------------------------------------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | foam-extend: Open Source CFD                    |
|  \\    /   O peration     | Version:     4.0                                |
|   \\  /    A nd           | Web:         http://www.foam-extend.org         |
|    \\/     M anipulation  | For copyright notice see file Copyright         |
\*---------------------------------------------------------------------------*/
Build    : 4.0
Exec     : interFoamtest
Date     : Oct 28 2019
Time     : 16:44:23
Host     : cfd
PID      : 116498
CtrlDict : "/home/cfd/foam/cfd-4.0/run/damBreak/system/controlDict"
Case     : /home/cfd/foam/cfd-4.0/run/damBreak
nProcs   : 1
SigFpe   : Enabling floating point exception trapping (FOAM_SIGFPE).

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
Create time

Create mesh for time = 0


PIMPLE: Operating solver in PISO mode


Reading g
Reading field pd

Reading field alpha1

Reading field U

Reading/calculating face flux field phi

Reading transportProperties

Selecting incompressible transport model Newtonian
Selecting incompressible transport model Newtonian
Calculating field g.h

Selecting turbulence model type laminar
time step continuity errors : sum local = 0, global = 0, cumulative = 0
PCG:  Solving for pcorr, Initial residual = 0, Final residual = 0, No Iterations 0
time step continuity errors : sum local = 0, global = 0, cumulative = 0
Courant Number mean: 0 max: 0 velocity magnitude: 0

Starting time loop

Courant Number mean: 0 max: 0 velocity magnitude: 0
Time = 0.001

PIMPLE: iteration 1
MULES: Solving for alpha1
Liquid phase volume fraction = 0.0247173  Min(alpha1) = 0  Max(alpha1) = 1
MULES: Solving for alpha1
Liquid phase volume fraction = 0.0247173  Min(alpha1) = 0  Max(alpha1) = 1
BiCGStab:  Solving for Ux, Initial residual = 1, Final residual = 8.84344e-16, No Iterations 1
BiCGStab:  Solving for Uy, Initial residual = 1, Final residual = 2.39687e-15, No Iterations 1
BiCGStab:  Solving for Uz, Initial residual = 0.999809, Final residual = 1.01154e-15, No Iterations 1
smoothSolver:  Solving for phiE, Initial residual = 1, Final residual = 0.00885022, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.00440562, Final residual = 0.00275942, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.00276397, Final residual = 0.00177986, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.00178161, Final residual = 0.00114823, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.00114896, Final residual = 0.000740514, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.000740817, Final residual = 0.000477462, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.000477588, Final residual = 0.000307809, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.000307862, Final residual = 0.000198419, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.000198441, Final residual = 0.000127897, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 0.000127906, Final residual = 8.24364e-05, No Iterations 1000
DICPCG:  Solving for pd, Initial residual = 1, Final residual = 0.0228419, No Iterations 2
DICPCG:  Solving for pd, Initial residual = 0.0113008, Final residual = 0.000494115, No Iterations 19
DICPCG:  Solving for pd, Initial residual = 0.00049866, Final residual = 2.39276e-05, No Iterations 115
DICPCG:  Solving for pd, Initial residual = 2.39472e-05, Final residual = 9.68596e-08, No Iterations 302
time step continuity errors : sum local = 9.29479e-09, global = 1.57022e-22, cumulative = 1.57022e-22
ExecutionTime = 30.3 s  ClockTime = 30 s

Courant Number mean: 0.000308178 max: 0.120588 velocity magnitude: 1.20588
Time = 0.002

PIMPLE: iteration 1
MULES: Solving for alpha1
Liquid phase volume fraction = 0.0247173  Min(alpha1) = 0  Max(alpha1) = 1
MULES: Solving for alpha1
Liquid phase volume fraction = 0.0247173  Min(alpha1) = 0  Max(alpha1) = 1
BiCGStab:  Solving for Ux, Initial residual = 0.776521, Final residual = 8.28489e-11, No Iterations 2
BiCGStab:  Solving for Uy, Initial residual = 0.488694, Final residual = 2.35091e-11, No Iterations 2
BiCGStab:  Solving for Uz, Initial residual = 0.492107, Final residual = 6.27383e-10, No Iterations 2
smoothSolver:  Solving for phiE, Initial residual = 8.24401e-05, Final residual = 5.31333e-05, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 5.31349e-05, Final residual = 3.42459e-05, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 3.42465e-05, Final residual = 2.20722e-05, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 2.20724e-05, Final residual = 1.42259e-05, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 1.4226e-05, Final residual = 9.16875e-06, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 9.1688e-06, Final residual = 5.90937e-06, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 5.90939e-06, Final residual = 3.80865e-06, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 3.80866e-06, Final residual = 2.45471e-06, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 2.45471e-06, Final residual = 1.58208e-06, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 1.58208e-06, Final residual = 1.01967e-06, No Iterations 1000
DICPCG:  Solving for pd, Initial residual = 0.146545, Final residual = 0.00361308, No Iterations 2
DICPCG:  Solving for pd, Initial residual = 0.00335961, Final residual = 0.000167276, No Iterations 105
DICPCG:  Solving for pd, Initial residual = 0.000188382, Final residual = 9.23987e-06, No Iterations 49
DICPCG:  Solving for pd, Initial residual = 9.8482e-06, Final residual = 9.46082e-08, No Iterations 286
time step continuity errors : sum local = 2.47934e-09, global = -3.54267e-22, cumulative = -1.97245e-22
ExecutionTime = 58.46 s  ClockTime = 58 s

Courant Number mean: 0.000218338 max: 0.0405799 velocity magnitude: 0.405799
Time = 0.003

PIMPLE: iteration 1
MULES: Solving for alpha1
Liquid phase volume fraction = 0.0247173  Min(alpha1) = 0  Max(alpha1) = 1
MULES: Solving for alpha1
Liquid phase volume fraction = 0.0247173  Min(alpha1) = 0  Max(alpha1) = 1
BiCGStab:  Solving for Ux, Initial residual = 0.431649, Final residual = 2.74542e-08, No Iterations 1
BiCGStab:  Solving for Uy, Initial residual = 0.223545, Final residual = 5.07216e-10, No Iterations 1
BiCGStab:  Solving for Uz, Initial residual = 0.212763, Final residual = 1.13065e-09, No Iterations 1
smoothSolver:  Solving for phiE, Initial residual = 1.01967e-06, Final residual = 6.57184e-07, No Iterations 1000
smoothSolver:  Solving for phiE, Initial residual = 6.57184e-07, Final residual = 4.23565e-07, No Iterations 1000
DICPCG:  Solving for pd, Initial residual = 0.027659, Final residual = 0.000699273, No Iterations 2
DICPCG:  Solving for pd, Initial residual = 0.00069462, Final residual = 3.42751e-05, No Iterations 109
DICPCG:  Solving for pd, Initial residual = 3.70155e-05, Final residual = 1.75277e-06, No Iterations 49
DICPCG:  Solving for pd, Initial residual = 1.78108e-06, Final residual = 9.77867e-08, No Iterations 266
time step continuity errors : sum local = 2.18185e-09, global = 1.21446e-22, cumulative = -7.57986e-23
ExecutionTime = 65.25 s  ClockTime = 65 s

Courant Number mean: 0.000237433 max: 0.0260814 velocity magnitude: 0.260814
Time = 0.004

PIMPLE: iteration 1
MULES: Solving for alpha1
Liquid phase volume fraction = 0.0247173  Min(alpha1) = -5.52899e-28  Max(alpha1) = 1
MULES: Solving for alpha1
Liquid phase volume fraction = 0.0247173  Min(alpha1) = 0  Max(alpha1) = 1
BiCGStab:  Solving for Ux, Initial residual = 0.212063, Final residual = 1.20667e-11, No Iterations 1
BiCGStab:  Solving for Uy, Initial residual = 0.157791, Final residual = 5.26792e-13, No Iterations 1
BiCGStab:  Solving for Uz, Initial residual = 0.144847, Final residual = 8.02311e-13, No Iterations 1
smoothSolver:  Solving for phiE, Initial residual = 4.23565e-07, Final residual = 2.73004e-07, No Iterations 1000
DICPCG:  Solving for pd, Initial residual = 0.00638702, Final residual = 0.000228527, No Iterations 2
DICPCG:  Solving for pd, Initial residual = 0.000229721, Final residual = 1.09143e-05, No Iterations 115
DICPCG:  Solving for pd, Initial residual = 1.142e-05, Final residual = 4.41946e-07, No Iterations 58
DICPCG:  Solving for pd, Initial residual = 4.43246e-07, Final residual = 9.98953e-08, No Iterations 236
time step continuity errors : sum local = 1.92551e-09, global = -2.38779e-22, cumulative = -3.14578e-22
ExecutionTime = 69.77 s  ClockTime = 69 s

Courant Number mean: 0.000307195 max: 0.0317014 velocity magnitude: 0.317014
Time = 0.005

PIMPLE: iteration 1
MULES: Solving for alpha1
Liquid phase volume fraction = 0.0247173  Min(alpha1) = 0  Max(alpha1) = 1
MULES: Solving for alpha1
Liquid phase volume fraction = 0.0247173  Min(alpha1) = 0  Max(alpha1) = 1
BiCGStab:  Solving for Ux, Initial residual = 0.141162, Final residual = 1.73043e-11, No Iterations 1
BiCGStab:  Solving for Uy, Initial residual = 0.123101, Final residual = 6.00829e-13, No Iterations 1
BiCGStab:  Solving for Uz, Initial residual = 0.11123, Final residual = 9.9712e-13, No Iterations 1
smoothSolver:  Solving for phiE, Initial residual = 2.73004e-07, Final residual = 1.75965e-07, No Iterations 1000
DICPCG:  Solving for pd, Initial residual = 0.0068371, Final residual = 0.000235051, No Iterations 2
DICPCG:  Solving for pd, Initial residual = 0.000232659, Final residual = 1.10913e-05, No Iterations 27
DICPCG:  Solving for pd, Initial residual = 1.12968e-05, Final residual = 5.32458e-07, No Iterations 125
DICPCG:  Solving for pd, Initial residual = 5.36239e-07, Final residual = 9.64374e-08, No Iterations 42
time step continuity errors : sum local = 1.68223e-09, global = 4.27902e-22, cumulative = 1.13324e-22
ExecutionTime = 74.91 s  ClockTime = 75 s

Courant Number mean: 0.000376038 max: 0.0360665 velocity magnitude: 0.360665

姑且假设我写的求解器没有大问题的条件下，上述结果说明，两个版本的求解结果存在了不同。
所以，我在想是不是of40和fe40的Laplace求解器在什么地方存在差异，导致了这样的结果？

李东岳

@cfd_lilili 在关于多相流的电势方程（Laplace方程）的求解问题中说：

fe4.0

这是啥。。。

cfd_lilili

@东岳 openFoam-extend4.0，不好意思，我以为这个是通用的简写

李东岳

@cfd_lilili 在关于多相流的电势方程（Laplace方程）的求解问题中说：

smoothSolver: Solving for phiE, Initial residual = 1, Final residual = 0.00666667, No Iterations 1000
smoothSolver: Solving for phiE, Initial residual = 0.969654, Final residual = 0.955898, No Iterations 1000
smoothSolver: Solving for phiE, Initial residual = 0.999906, Final residual = 0.999906, No Iterations 1000
smoothSolver: Solving for phiE, Initial residual = 0.999943, Final residual = 0.999943, No Iterations 1000
smoothSolver: Solving for phiE, Initial residual = 0.999959, Final residual = 0.999959, No Iterations 1000
smoothSolver: Solving for phiE, Initial residual = 0.99997, Final residual = 0.99997, No Iterations 1000
smoothSolver: Solving for phiE, Initial residual = 0.999977, Final residual = 0.999977, No Iterations 1000
smoothSolver: Solving for phiE, Initial residual = 0.999982, Final residual = 0.999982, No Iterations 1000
smoothSolver: Solving for phiE, Initial residual = 0.999986, Final residual = 0.999986, No Iterations 1000
smoothSolver: Solving for phiE, Initial residual = 0.999989, Final residual = 0.999989, No Iterations 1000

你在求解一个方程求解多次。另外，迭代次数1000，没有收敛，

这是一个非常简单的方程，你需要更细心的debug

cfd_lilili

@东岳谢谢老师
我把代码换了写法，问题就解决了
这是原来的写法

        fvScalarMatrix phiEEqn
        (
            fvm::laplacian(  phiE )
        );

        phiEEqn.relax();
        solve(phiEEqn);

把它简单地写为

    solve( fvm::laplacian(sigmaE, phiE) );

问题勉强算解决了，但还不知道之前的问题出在哪。

李东岳

后来这个解决了吗 :-)

gzs20

老师，请教一下，不同相的交界面电势的边界条件采用的那种了

李东岳

但其电导系数（sigma）在不同的相中具有不同的值。

我去年在笔记的附录中整理了这部分内容。这部分采取多计算域的方法处理比较好。

gzs20

@李东岳东岳老师，您好，请问您说的笔记的附录在哪里可以找到，告知一下，目前卡在了电势的求解这一步

李东岳

http://dyfluid.com/index.html 主页有下载

gzs20

@李东岳谢谢东岳老师

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关于多相流的电势方程（Laplace方程）的求解问题