I'm very new to CFD and I'm trying to write my own compressible viscous flow solver. I applied the MacCormack algorithm to the Navier-Stokes equations, but I'm not sure how to proceed from a programming standpoint. For each point (i,j) I have the discretized equations for mass, momentum, energy, and an equation of state. How do I solve the equations since they are coupled? Any help I could get would be great. Thanks.

Computational Fluid Dynamics: The Basics with Applications by John David Anderson

The differences between the sequences which mass, velocity and energy is solved are not large.

In my case, I used to compute the density as rho_n+1=rho_n+Frho(rho,u)_n where Frho stands for the mass flux

the momentum m=rho*u as m_n+1=m_n+Fm(rho,u,p)_n

the energy E=rho*e e_n+1=e_n+Fe(rho,u,p,e)_n

in the in-house DGM code.

But you can use the different way as First, the density is found by Frho_n Second, the momentum is computed by Fm(rho_n+1,u_n,p_n) Third, the energy is compute by Fe(rho_n+1,u_n+1,p_n,e_n)

However, there are no big difference of results whether one use either n+1 or n

These are just my experiences, not standard.

Good luck

Perfect! Thanks so much.