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李老师，还是这个模块，能不能再问下这个临近单元的预测速度是怎么得到的？不也是未知数吗？如果是的话，那么方程13是不是把所有的网格的体心上的值联立在一起求得的？

感谢李老师解答，但是我还是不太明白您说的意思，您在网页中说方程21是经过方程18移项得到，所以我觉得更应该是我下边图片中推导的形式，您单单在网页中写了一个移项得到，可能因为我基础薄弱，没能理解怎么就从第n+1个时间步跳到第n个时间步了，还望李老师不吝赐教，感谢

为什么公式21中第N个网格单元的体心上的速度值是第n个时间步而不是第n+1个时间步上的值？还请李老师亦或各位大佬不吝赐教

第一次在这个网站上求助各位大佬，报错图片不知道怎么看不了了，不好意思![IWE)}@6(NH98E9LRH@PDEK.png

下附CourantNo.H文件内容

/*---------------------------------------------------------------------------*\
  =========                 |
  \\      /  F ield         | foam-extend: Open Source CFD
   \\    /   O peration     | Version:     5.0
    \\  /    A nd           | Web:         http://www.foam-extend.org
     \\/     M anipulation  | For copyright notice see file Copyright
-------------------------------------------------------------------------------
License
    This file is part of foam-extend.

    foam-extend is free software: you can redistribute it and/or modify it
    under the terms of the GNU General Public License as published by the
    Free Software Foundation, either version 3 of the License, or (at your
    option) any later version.

    foam-extend is distributed in the hope that it will be useful, but
    WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
    General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with foam-extend.  If not, see <http://www.gnu.org/licenses/>.

Global
    CourantNo

Description
    Calculates and outputs the mean and maximum Courant Numbers.

\*---------------------------------------------------------------------------*/

scalar CoNum = 0.0;
scalar meanCoNum = 0.0;
scalar velMag = 0.0;

// HR 26.06.18: A parallel run has at least two cells and therefore at least
// one internal face in the global mesh. It may be a processor boundary, but
// this is captured by max(mag(phi)).
// Old formulation hangs on parallel cases where one partition is degenerated
// to a single cell.
if (mesh.nInternalFaces() || Pstream::parRun())
{
    surfaceScalarField magPhi = mag(phi);

    surfaceScalarField SfUfbyDelta =
        mesh.surfaceInterpolation::deltaCoeffs()*magPhi;

    const scalar deltaT = runTime.deltaT().value();

    CoNum = max(SfUfbyDelta/mesh.magSf()).value()*deltaT;

    meanCoNum = (sum(SfUfbyDelta)/sum(mesh.magSf())).value()*deltaT;

    velMag = max(magPhi/mesh.magSf()).value();
}
else
{
    // Single cell mesh: Co is still defined; use cell formulation

    const scalar deltaT = runTime.deltaT().value();

    const scalar deltaX = Foam::cbrt(mesh.V()[0]);

    // recover velocity field in a more general way
    const volVectorField& URef
	    = mesh.db().lookupObject<const volVectorField>("U");

    velMag = mag(URef[0]);

    CoNum = velMag*deltaT/deltaX;

    meanCoNum = CoNum;
}

Info<< "Courant Number mean: " << meanCoNum
    << " max: " << CoNum
    << " velocity magnitude: " << velMag
    << endl;

// ************************************************************************* //

#include "fvCFD.H"
#include "MULES.H"
#include "subCycle.H"
#include "interfaceProperties.H"
#include "twoPhaseMixture.H"
#include "turbulenceModel.H"
#include "dynamicFvMesh.H"
#include "pimpleControl.H"
#include "immersedBoundaryPolyPatch.H"
#include "immersedBoundaryFvPatch.H"
#include "emptyFvPatch.H"

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

int main(int argc, char *argv[])
{
#   include "setRootCase.H"

#   include "createTime.H"
#   include "createDynamicFvMesh.H"

    pimpleControl pimple(mesh);


#   include "readGravitationalAcceleration.H"


#   include "initContinuityErrs.H"
#   include "createIbMasks.H"
#   include "createFields.H"
#   include "createControls.H"
#   include "correctPhi.H"
#   include "CourantNo.H"
#   include "setInitialDeltaT.H"

我在foamextend5.0环境下编写具有IBM方法的两相流求解器，是在foamextend5.0自带的求解器pimpleDyMIbFoam基础上修改的，以上是一部分主程序代码，我在foam extend5.0环境下编译这个求解器，显示如下错误，是在我上边发的代码的第33行
请问各位大佬应该这么修改呢？我确定这个报错路径下的CourantNo.H文件是没有问题的，因为这是系统路径下的文件啊，我也没有修改过，之前使用过这个文件编译其他求解器，也是没有问题的，所以现在不知道问题出在哪里了？
还请各位老师不吝赐教