[FrancescoRizzuto]

Hi All,
I am looking for some reference or advice on Compressible Fluid. I am working in Cavitation Field and trying to create a one dimensional Numerical solver, but i have problem in the resolution of the continuity equation. Although the x momentum i can solve it in Conservative form, for the continuity equation i have no idea how can i solve it in order to use it in PISO or Simple methods.
Moreover, the explicit methods seems the easier for High resolution scheme as MUSCL/TVD scheme but can some advise me how can i pass this model in implicit way? the fluxt limiter in the implicit way should be consider the velocity on previous time step or should in some way goes in the systems?
Furthermore, the equation of the energy are strictly necessary considering the Fluid isothermal, can i close the system withg the bulk equations?
Regards