About the Flux splitting method

maximus

hi,I am try to solve the dilute gas-particle problem.In the mathematical model I neglect the pressure of partile and the engergy equation.The interaction between the gas and particle is modeled with the drag term.This is a very common dilute gas-particle model,and they are Eulerian equations.The main difference between this model and the Euler equations is the absence of pressure term. The eigenvalues of the equations are the same(lemda(1,2,3)=u for the characteristic matrix in x direction,and lemda(1,2,3)=v in the y direction) ,this sytem is not a strict hyperbolic system.I used to solve N-S equation with the pressure-based SIMPLE method, so I am not familiar with the density based mathod. I have reviewed some relative books on the solution of hyperbolic equations. The most common method is the Flux spliting method which always involes the split of Jacobian matrix. But the dilute gas-droplet equations is not a srtick hyperbolic system, So my question is whether the flux spliting method can be used to solve this equations? Are there some more suitable other methods? Also does anybody can give me a explanation on the relation of the flux spliting method,MUSCL and AUSM. Are they three kinds of independent splitting method,or sometimes they can work with each other? Thanks for any response!! Maximus