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Finite Volume Method for calculation of compressible fluid

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Finite Volume Method for calculation of compressible fluid

Posted January 29, 2010 at 12:31 by kirilhs
Updated July 4, 2012 at 12:30 by kirilhs

Hi everyone,

In the
Department of "Mathematical Modeling and Numerical Simulations", Institute of Mechanics - BAS, is developed a new finite volume algorithm for calculation of compressible fluid (SIMPLE-TS (Time Step). The algorithm is published in Journal of Computational Physics.
SIMPLE-like algorithms have one main disadvantages. They use the approximation drho/dt = (rho - rho^(n-1))/ht in the pressure equation. Because if this disadvantages the pressure equation do not satisfy the sufficient condition for convergence of the iterative method and to ensure the convergence one has to use the under-relaxation coefficients and also to work carefully with the number of iteration, when pressure equation are solved in the iteration procedure. This problem is solved in PISO, with substitution of density with pressure using equation of state. This idea is used in SIMPLE-TS. We prove that in this way the pressure equation satisfy
the sufficient condition for convergence of the iterative method and here are no needs of under relaxation coefficients. Furthermore it is shown with appropriate problem that the bad influence of the convergence of the term drho/dt = (rho - rho^(n-1))/ht is valuable independent of speed of fluid flow.
In the algorithm SIMPLE-TS the pressure equation and the energy equation are calculated in one internal loop, before final calculation of velocities.
The algorithm SIMPLE-TS is simple and is easy to be organized parallel.
Direct comparison shows that SIMPLE-TS is faster then SIMPLE and PISO.
The accepted manuscript, source code written on C++ and presented problems in the paper are freely available on the web side of the Department of "Mathematical Modeling and Numerical Simulations", Institute of Mechanics - BAS. The program can be used to calculate unsteady and steady 2D fluid flows for simple rectangular shapes.
The program can calculate the flows at all speeds.
It is available the problem of flow past a square moving in a microchannel at Mach number 2.43. All shock waves are well calculated and the results are compared with DSMC.
The code can be run on MPI. It is used non-blocking communications and the reached speed-up is close to idle, for relatively large problems of course.

New version will be published to the end of 2012. In new version is used TVD schemes Min-Mod, QUICK and SUPERBEE for approximation of convective terms. The scheme use 4^2 = 16 to 8^2 = 64 times less cells in computational domain, for calculation of supersonic (Mach number 2.43) flow past square in a microchannel. This increase computational time many times.

The source is of new version v.1.1 (August, 2011) is available from here.
The new version 1.1, since August, 2011 is with improved parallel performance.

If you have any questions or suggestions feel free to ask.
Tell me your opinion for the algorithm.

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Total Comments 7


  1. Old Comment
    hello what is your suggests book me,
    for study the nanofluid by method multiphase
    Posted July 19, 2011 at 09:46 by parsad parsad is offline
  2. Old Comment
    Could you describe the question in more details?
    Posted July 20, 2011 at 07:28 by kirilhs kirilhs is offline
  3. Old Comment
    This scheme seems very interesting.

    How does this solver perform at relatively low mach number (eg oceanography), where compressible effects can be ignored ? How easy to adapt to applications where the Boussinesq approximation is used ? or with the shallow water equations ?
    Posted July 29, 2011 at 08:36 by bouloumag bouloumag is offline
  4. Old Comment
    According to my experience there is no problem with any speed including very slow one. The algorithm is also used to calculate incompressible Navier-Stokes equations.
    I have no experience with Boussinesq approximation or shallow water equations.
    My opinion is that the algorithm is applicable for this problems. I think that the application to this problems will be relatively easy. If you mean the similar system of equations like this one (Conservative form):

    You can translate the system of equations to be the same as equations used to derive the numerical scheme. Next have to be removed redundant terms in the algorithm and the parameters have to be equivalent.
    If You have any questions feel free to ask.
    Posted July 29, 2011 at 13:26 by kirilhs kirilhs is offline
  5. Old Comment
    Can I use this method in fluent?how I do?
    Posted November 27, 2011 at 08:31 by mohammad88 mohammad88 is offline
  6. Old Comment
    Yes, if Fluent implemented SIMPLE-TS in their code. I do not use Fluent at the moment and can not tell You the answer of this question.
    The Fluent is commercial software and You can not implement algorithm by yourself.
    You can ask Fluent is the algorithm SIMPLE-TS already available in their code or will be in the future.
    Posted November 27, 2011 at 09:10 by kirilhs kirilhs is offline
  7. Old Comment
    Can you try to explain it, through the flow-chart? Actually, I didn't understand how you are trying to implement the code?

    Thanks in advance.
    Posted April 1, 2013 at 01:42 by Tushar@cfd Tushar@cfd is offline

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