[bearcat]

Anyone has the experience in coding CFD using FEM?

I am on my beginning on this. But I find that coding FEM for CFD is a very tough job, particularly in deriving the stiff matrix coefficients. Suppose we use Q1Q1 element for a 2D incompressible flow problem in a coupled way, we have u, v, p as unknown and 4 nodes in one elements using SUPG or GLS and equal order interpolation. Then the stiffness matrix will be 12 x 12 for each element. In 3D case, that will be 8 nodes and a 32 x 32 matrix. Then we need to numerically integrate 32 x 32 = 1024 coefficients, each with different expressions, all nonzero and derived by hand. If we use least-square finite element method, the expressions will be even more complicated.

Is my understanding correct? How do people code CFD by FEM?

Thank you.

BTY, if we use equal order interpolation, does that mean the same shape function for velocity and pressure?