Force on cylinders through momentum balance
 

Hello

I'm developing a CFD 2D finite element method code in my PhD thesis. I'm interested in vortex shedding vibrations of cylinders. In this way I want to calculate forces acting over the cylinder. Besides the conventional integration of tensions due to pressure and velocities over the cylinder wall, I'm also using the balance of momentum approach. This approach is convenient because the matrices are already assembled and it avoids errors in the integration of the cylinder wall. But I'm having some problems. I assembled the matrix equations in order to attain the forces in x and y directions as a nodal quantity. The LHS is composed of a vector of nodal force components times a mass matrix integrated over the Dirichlet boundaries of the problem.(See page 860 of the book of P. Gresho) My questions are: 1) After obtaining the nodal force components how can I get the total force acting over the body? 2) If I have two bodies in the problem, can I use this method to obtain forces in each body ? Can I generate the mass matrix for each body or I have to integrate this mass matrix over all Dirichlet boundaries that are present in the problem?

Thanks, Mauro