Finite Volume Method for calculation of compressible fluid
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 (SIMPLETS (Time Step). The algorithm is published in Journal of Computational Physics.
SIMPLElike algorithms have one main disadvantages. They use the approximation drho/dt = (rho  rho^(n1))/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 underrelaxation 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 SIMPLETS. 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^(n1))/ht is valuable independent of speed of fluid flow.
In the algorithm SIMPLETS the pressure equation and the energy equation are calculated in one internal loop, before final calculation of velocities.
The algorithm SIMPLETS is simple and is easy to be organized parallel.
Direct comparison shows that SIMPLETS 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 nonblocking communications and the reached speedup 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 MinMod, 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.
email: kshterev@yahoo.com, kirilhs@yahoo.com, kshterev@imbm.bas.bg
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 (SIMPLETS (Time Step). The algorithm is published in Journal of Computational Physics.
SIMPLElike algorithms have one main disadvantages. They use the approximation drho/dt = (rho  rho^(n1))/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 underrelaxation 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 SIMPLETS. 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^(n1))/ht is valuable independent of speed of fluid flow.
In the algorithm SIMPLETS the pressure equation and the energy equation are calculated in one internal loop, before final calculation of velocities.
The algorithm SIMPLETS is simple and is easy to be organized parallel.
Direct comparison shows that SIMPLETS 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 nonblocking communications and the reached speedup 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 MinMod, 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.
email: kshterev@yahoo.com, kirilhs@yahoo.com, kshterev@imbm.bas.bg
Total Comments 7
Comments

hello what is your suggests book me,
for study the nanofluid by method multiphasePosted July 19, 2011 at 09:46 by parsad 
Could you describe the question in more details?
Posted July 20, 2011 at 07:28 by kirilhs 
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 
According to my experience there is no problem with any speed including very slow one. The algorithm is also used to calculate incompressible NavierStokes 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):
http://en.wikipedia.org/wiki/Shallow_water_equations
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 
Can I use this method in fluent?how I do?
Posted November 27, 2011 at 08:31 by mohammad88 
Yes, if Fluent implemented SIMPLETS 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 SIMPLETS already available in their code or will be in the future.Posted November 27, 2011 at 09:10 by kirilhs 
Can you try to explain it, through the flowchart? 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