correctBoundaryConditions里修正面心梯度的公式没看明白

Cp_Zhao

代码在src/finiteVolume/finiteVolume/gradSchemes/gaussGrad/gaussGrad.C144行：

template<class Type>
void Foam::fv::gaussGrad<Type>::correctBoundaryConditions
(
    const GeometricField<Type, fvPatchField, volMesh>& vsf,   
    GeometricField
    <
        typename outerProduct<vector, Type>::type, fvPatchField, volMesh
    >& gGrad
)
{
    typename GeometricField
    <
        typename outerProduct<vector, Type>::type, fvPatchField, volMesh
    >::Boundary& gGradbf = gGrad.boundaryFieldRef();

    forAll(vsf.boundaryField(), patchi)
    {
        if (!vsf.boundaryField()[patchi].coupled())
        {
            const vectorField n
            (
                vsf.mesh().Sf().boundaryField()[patchi]
              / vsf.mesh().magSf().boundaryField()[patchi]
            );

            gGradbf[patchi] += n *
            (
                vsf.boundaryField()[patchi].snGrad()
              - (n & gGradbf[patchi])
            );
        }
     }
}

里面vsf应该是待求梯度的场吧、然后gGradbf是根据体心梯度插值得到的面心梯度、n是面单位法向、.snGrad()是$\frac{\phi_{f}-\phi_{C}}{d_{Cf}}$ ?
这个面心梯度的修正公式怎么来的我还是没看懂：

gGradbf[patchi] += n *
(
    vsf.boundaryField()[patchi].snGrad()
  - (n & gGradbf[patchi])
);

Cp_Zhao

自己翻书找到答案了，《The FVM in CFD(OpenFOAM, Matlab)》那本书Page 303有讲到：
选区_001.png

东岳

感谢分享！！