That code was based on Euler equations for simulating underwater explosions consisting of explosive gas and water. Due to complex physics behind explosions, the entire process ranges from compressible to incompressible. Unfortunately, compressible code cannot deal with incompressible phase due to instability. Could anyone advice me how to include these incompressible feature using a compressible code?

Need to know a bit about the compressible code.

Density or pressure based?

FD, FV, FE?

EOS (ideal gas mixture)?

Is the gas treated as distributed through the water or are there two distinct phases (I guess not)?

Sorry for mess.

It was a density-based code. The space was discretized with the discontinuous Galerkin method(DGM) which is similar to the FV. The explosive gas was modeled by the JWL EOS and water was modeled by the Tait EOS. The material interface was tracked by the level set method. The material interface between two fluids was treated by a ghost fluid method which is a two fluid sharp interface method. Thanks for your concern.

The problem was that in early time which may be in compressible state the code worked well, but as time goes, the code was diverged.

Can you introduce artificial compressibility, e.g. finite sound speed when simulating the incompressible part of the simulation?

Current code does not consider artificial compressibility? In fact, the scope of phd work is compressible phase only. I wish to extend the applicability of current code to the incompressible phase as well. It may lead to the use of partitioned matrix or similar things to avoid stability problem. I know this is an active research area yet but I wish to add these into the current code because I suffered from stability problems as time goes. That is also general that the compressible solver based on density formaluation causes stability problems since the Mach number may become lower than 0.3.

Dear Jinwon,

You need to look into preconditioning, which can help you extend the compressible flow solver into the incompressible limit. Possibly the following paper might be of interest to your present concern,

"All speed time-accurate underwater projectile calculations using a preconditioning algorithm", Michael Dean Neaves and Jack. R. Edwards, J. of Fluids Engg. Transactions of the ASME, Vol. 128, pp 284-296, March 2006.

Hope this helps

Regards,

Ganesh

I strongly agree with Ganesh. You do need to implement the preconditioning technique. If I understand correctly, your is a two-phase flow.

I would suggest the following paper:

Shin et al, "Application of preconditioning technique to gas-liquid two-phase flow computations", Journal of Fluids Engineering, 126:605-612,2004.

Is your code explicit or implicit time marching?

Low Mach number preconditioning is exactly what you need. Good luck...

Dear NRD! Could you send that paper by email to jwpark1@gmail.com? I do not have resource to download from somewhere. The "Sciencedirect" does not provide that paper. Thanks in advance! My code is explicit time marching.

"COMBINATION OF COMPRESSIBLE AND INCOMPRESSIBLE FLOW CODES VIA IMMERSED METHODS"

Rainald Löhner, Philippe Ravier, Pierre de Kermel and Jean Roger

Might be helpful.

/F.P.