Can AC be substituted in a compressible solver?.. In the literature, pressure is computed by p=c^2*density----------------(1)

For incompressible phase, eqn(1) is used to determine the pressure.

Aboves are generally mentioned in many references. However, I do not know how to implement it in my current codes.

Have you seen this kind of approach to extend a compressible solver for incompressible computation?

This approach is used when you want to use the incompressible solver and want to satisfy the continuity. That c is an artificial speed of sound. For compressible solvers people use similar ideas when they do preconditioning.

Can I ask you the approach compressible methods have used?

I cannot understand well the last sentence.

Thanks in advance!

The method used for compressible flows is preconditioning which is carried out by multiplying with a matrix referred as preconditioning matrix.For certain forms of the matrix the equations of incompressible solver using artificial compressiblity and modified navier stokes equations look very similar.

Can I ask your a good reference on the comment you gave?..

I have read about some similarities in the book of anderson et. al," Computational fluid mechanics and heat transfer " Chapter 9

I assume you currently have an explicit compressible code with low speed stagnant regions which are causing problems? You refer to instability in these regions which suggests you are using a variable time step and using the local velocity and not the speed of sound in determing a suitable time step. Is this correct?

If you are only interested in a steady state solution and not a transient solution then you can essentially fiddle things by lowering the speed of sound in the "incompressible" regions and sticking with an explicit scheme. This will probably reduce the required number of iterations a noticeable amount but is unlikely to do anything dramatic.

To get good performance you need an implicit step to handle the stiff terms on the RHS of the momentum and energy equations in conjunction with updating the continuity equation.

I assume you currently have an explicit compressible code with low speed stagnant regions which are causing problems?

--> Yes. I am using a Runge-Kutta Discontinuous Galerkin method for Euler equations to solve the fluid flow induced by explosion.

You refer to instability in these regions which suggests you are using a variable time step and using the local velocity and not the speed of sound in determing a suitable time step. Is this correct?

--> Yes or No. I determined the time step by delt=MIN(dx,dy)/MAX(u+c)*CFL. As far as I know, that formular is commonly used in CFD communities. In summary, to determine the time step size, I am using both the local velocity u and the speed of sound c.

If you are only interested in a steady state solution and not a transient solution then you can essentially fiddle things by lowering the speed of sound in the "incompressible" regions and sticking with an explicit scheme.

--> No. I am intersted in total solution including transient solutions in compressible phase and almost steady state solutions in nearly incompressible phase. How can I make the speed of sounder lower?

To get good performance you need an implicit step to handle the stiff terms on the RHS of the momentum and energy equations in conjunction with updating the continuity equation.

--> Can you let me know how I include such an implicit step in current code? I could not find any reference.

> No. I am intersted in total solution including transient solutions in
: compressible phase and almost steady state solutions in nearly
: incompressible phase. How can I make the speed of sounder lower?

Do you mean phase as in solid, liquid and gas? In which case, what phases have you got?

If you want a transient solution then you cannot alter the speed of sound or else you will not solve your governing equations. It is only a technique for accelerating the convergence to steady state but can be used sometimes in an inner loop of an implicit time stepping solution procedure taking large time steps. Since you are using small time steps with an explicit scheme it would appear to be an irrelevant technique.

> Can you let me know how I include such an implicit step in current code? I
: could not find any reference.

There are billions of references. Implicit codes have been widely used since the 1960s. In fact, one of the good places to look is probably the T-3 group at Los Alamos who studied explosions in the 1960s and first wrestled with and solved the problems you are probably looking at. Look up, for example, the description of the ICE or YAQUI codes. The reports usually included the FORTRAN program statements.