FEM pressure poisson equation (Implicit)

cfd-beginner

Hello,

I need your help guys. I currently use a explicit code for solids. Instead of calculating the stress by a solid constitutive equation, I calculate now the stress of a newtonian fluid, where the pressure is calculated implicitely.

FEM pressure poisson equation: LP = (1/dt) D + fp where L = laplace matrix = B*B^T P = kinematic pressure = p/rho dt = delta t D = N*(grad v) N = shape functions fp = N (dp/dn)

Am I correct (implict part of code)? 1. for each 4-node quadrilateral element, the LHS is a matrix(L) 4x4 and a vector P 4x1? 2. I need to assamble (1.) into a global system leading to a matrix nodenum x nodenum, right?

Thank you for any help! Rafa