Regarding pressure projection method for unsteady viscous compressible flow
 

Hi
i have searched many of the papers related to pressure projection method for unsteady viscous compressible flow with finite volume method and staggered grid approach. But most of them deal with incompressible flow. Please help me out with exact solution to my problem.

please, clarify better what is your problem .... what do you mean for "exact solution" :confused:

Regarding pressure projection method
 

most of the papers that i have searched are for incompressible flows....i want papers related to unsteady viscous compressible flow with pressure projection method....thx

The projection method is based on Helmholtz-Hodge decomposition that any vector can decompose into a divergence-free vector and a potential of a scalar function.

I don't think projection method can be used in your study, because it cannot satisfy this condition, div.V =0.

I works on incompressible flow, so I am sorry if I make some mistakes.

I agree! It is a method to project the intermediate velocity field onto the subspace of divergence-free vector field, conversely for compressibla flows you have to solve the full continuity equation d/dt rho + div ( rho V) = 0 coupled with momentum and energy equation. The pressure is a state variable, not a lagrangian multiplier as it is in incompressible flows.

Method for solving compressible flows are different, as example see the PISO method

Regarding pressure projection method for compressible flow
 

Does anybody have information on research papers related to unsteady viscous compressible flow....?

see these books:

Ferziger J H , Peric M Computational Methods For Fluid Dynamics (Springer, 3Ed, 2001)

Chung T.J. Computational fluid dynamics (CUP, 2002)

Regarding pressure projection method
 

Books are somewhat useful but i have few doubts:
In one of the paper it was mentioned that CBS(Characterized Based Split procedure) is the basis of pressure projection method. In pressure projection method for incompressible flow we calculate intermediate velocity by ignoring pressure related terms. And in the second step we calculate for pressure using pressure poisson equation.
Somewhat similar kind of procedure is mentioned in Fractional step method.
I am really getting confused between pressure projection method and fractional step method and CBS scheme.....Please help me out with the pressure projection method for unsteady viscous compressible flow....? i have just started working on this project so that's why new terms are creating more doubts in my mind....please help me thx for your suppport

Check this:

No Hillike formally you are completely right ! I agree with you. However I have seen somewhere a kind of method similar to the projection method which was adapted to compressible flows. I have to check....

But why do you need to use projection method or any kind of coupling algorithm designed for incompressible flows for compressible flow? Indeed for compressible flows you have the equation of state to compute the pressure.
I recall that for incompressible flow the purpose of such methods (projection, piso, simple, etc...) is to compute the pressure since you do not have any equation for that.
In compressible flow, integrate the continuity equation to get the density, integrate the energy equation to got energy or temperature, then use equation of state to get the pressure. No need to use any sort of coupling algorithm...
Even if it is true that one can use piso, simple, etc...for compressible flows the idea of that was to use a kind of unified method whatever the flow is incompressible or compressible. Then using the same code you can solve incompressible or compressible flows. But it is not necessary.

Regarding pressure projection method
 

As a part of project my project guide have asked me whether it is possible to do it or not....my senior have done the same thing using simple algorithm but the problem came when method failed to capture the shocks with good resolution.

The main framework of the projection method (fractional step is also a valid and common terminology but it is more general) is, as previously stated by others, the Helmholtz-Hodge decomposition.

Very roughly, in that framework it is stated that a general vector field can be decomposed as the sum of two vector fields, one providing for the correct curl and the other for the correct divergence. The two of them are shown to be the solutions of two different differential problems, each requiring for specific boundary conditions.

Now, there is no requirement on the divergence of the vector field, which can also be different from zero. Here probably comes the confusion. For a compressible flow (high Mach number, acoustic and convective velocity scales being comparable), as also already stated, there is no actual need for a projection as you already have all the required prognostic equations.


This is different from the case with variable density, where you still have a nearly divergence free velocity field but that is no more your continuity equation. Also, you may want an efficient algorithm that without outer iterations can perform well in both incompressible and compressible cases. Or, like in the paper i cited above (which i still suggest you to read), for taking into considerations the coupling between the pressure and the energy equation.

However, i don't know if your specific case (e.g., shock waves) can really be handled by such non-iterative algorithms. I guess not. Also, there could be several reasons for the shocks not being properly captured. The pressure-velocity coupling would not be my first guess.

I totally agree with Paolo !! I would have said exactly the same thing.
If you have somme difficulties with shock capturing the problem is probably somewhere else...I would more incriminate your convection scheme, or grid resolution, or time stepping or both...;)

I totally agree with Paolo, too ...
I wonder if the confusion is in the temrinology "projection" ... I'm thinking about the "weak form" of the equations that can be shown to be obtained by means of a suitable projection along test-functions (as in FEM and FV).

:confused::confused:

Results for how to obtain pressure equation for unsteady viscous compressible flow
 

here is the link for the pressure equation for mentioned flow condition....
http://www.scribd.com/doc/27927305/7...quation-in-Com
The resultant set of equations can be solved directly But still some modifications like intermediate velocity has to be introduced in this method to convert it into pressure projection method & may be with the same by using semi-implicit for first part and fully implicit for second part advantage of using somewhat large time step can be used....thank you for your support.

This is not a projection method but an algorithm for compressible flow that have coupled variables ... you need to explore SIMPLE and PISO methods

No i mean to say some modifications like
The intermediate velocity is calculated with the pressure not included. This is the major difference to SIMPLE type methods:It include the pressure gradient in the Navier-Stokes equation, so you only need to solve the poisson equation for the pressure correction.
The procedure for the projection method is (with explicit time treatment for the velocities):
- calculate intermediate velocity u* without the pressure gradient
- calculate the divergence of the velocity field, this term will be the right hand side of the poisson equation for the pressure
- discretize the poisson equation for the pressure (trivial for constant density)
- solve the poisson equation iteratively
- correct the velocities (explicitly) with the pressure gradient
- go to next timestep

I totally quote Filippo. Indeed, it is more or less the same method the senior you cited is already using (unless he is doing something wrong). The PISO cited in these notes is somehow different from the simple (and also applicable in a non-iterative fashion) but definitely not a projection method in its classical sense.

Then will you please guide me about classical pressure projection method for the same....? My senior did the same with SIMPLE algorithm and he got the results but method failed to capture shocks with good resolution. So i have to verify that whether pressure projection method can do better or not.