# 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.
e-mail:
kshterev@yahoo.com, kirilhs@yahoo.com, kshterev@imbm.bas.bg

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