[gmori]

Hi,everyone.

I would like to use the OpenFOAM function LUsolve, but I don't know how to use it.

After studying the code in which LUsolve is used, it seems that, for example, if one wants to solve the simultaneous linear equation Ax=b, one can use the statement LUsolve(A,x), where b is added to x in such a way that it is transferred to the left side. I do not understand why b is added to x. The code for the viewfactor method I referred to is as follows

if (Pstream::master())
{
// Variable emissivity
if (!constEmissivity_)
{
scalarSquareMatrix C(totalNCoarseFaces_, 0.0);

for (label i=0; i<totalNCoarseFaces_; i++)
{
for (label j=0; j<totalNCoarseFaces_; j++)
{
const scalar invEj = 1.0/E[j];
const scalar sigmaT4 =
physicoChemical::sigma.value()*T4[j];

if (i==j)
{
C(i, j) = invEj - (invEj - 1.0)*Fmatrix_()(i, j);
q[i] +=
(Fmatrix_()(i, j) - 1.0)*sigmaT4 + qrExt[j];
}
else
{
C(i, j) = (1.0 - invEj)*Fmatrix_()(i, j);
q[i] += Fmatrix_()(i, j)*sigmaT4;
}

}
}

Info<< "Solving view factor equations for band :"
<< bandI << endl;

// Negative coming into the fluid
LUsolve(C, q);
}

Here it is trying to solve the equation Cq=b,
where:
Cij = deltaij/Ej - (1/Ej - 1)Fij
q = heat flux
b = A eb - Ho
and:
eb = sigma*T^4
Ej = emissivity
Aij = deltaij - Fij
Fij = view factor matrix

Can someone please tell me how to use LUsolve in detail?
Thank you in advance.

[jherb]

Have a look at this thread: How to solve linear equations in codedFixedValue boundary?

It shows two different ways for solving linear equations in OpenFOAM. One if you want to solve for a vector in each cell of your mesh based on a 3x3 matrix and a vector and another for a generic square matrix.

[gmori]

Hi,jherb.
Thank you for your reply.
I will refer to the thread you indicated.