You can read a short abstract below for my paper Pressure based finite volume method for calculation of compressible viscous gas flows.

Abstract: A pressure based, iterative finite volume method is developed for calculation of compressible, viscous, heat conductive gas flows at all speeds. The method does not need the use of under-relaxation coefficient in order to ensure a convergence of the iterative process. The method is derived from a general form of system of equations describing the motion of compressible, viscous gas. An emphasis is done on the calculation of gaseous microfluidic problems. A fast transient process of gas wave propagation in a two-dimensional micro-channel is used as a benchmark problem. The results obtained by using the new method are compared with the numerical solution obtained by using SIMPLE (iterative) and PISO (non-iterative) methods. It is shown that the new iterative method is faster than SIMPLE. For the considered problem the new method is slightly faster than PISO as well. Calculated are also some typical microfluidic subsonic and supersonic flows, and the Rayleigh–Bénard convection of a rarefied gas in continuum limit. The numerical results are compared with other analytical and numerical solutions.

The algorithm SIMPLE-TS (Time Step) is published in [1].

The accepted manuscript can be downloaded from here, the paper in it`s final mode is available here.

The source code ver. 1.1 of the algorithm SIMPLE-TS written in C++ and the short help (release date: August, 2011).

Notes:

– The parallel organization is according [4].

– The parallel efficiency is improved according v1.0 (see [4]).

– The bugs of the code, when are used more then 20 CPU are solved.

The source code ver. 1.0 of the algorithm SIMPLE-TS written in C++ and the short help (release date: January, 2010).

Notes:

– The parallel organization is according [2].

Problems:

Pressure driven gas flow in a microchannel – the problem is defined in [1]

Unsteady pressure driven gas flow in a microchannel – the problem is defined in [1]

Flow past a confined squaree in microchannel – Mach number 0.1 – the problem is defined in [1] (file 1 and file 2)

Flow past a confined square in a microchannel – Mach number 2.43, space step 0.05 – the problem is defined in [1]

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Unsteady supersonic, compressible, viscous, heat-conductive fluid flow past a confined square in a micro-channel – Mach number 2.43 and Knudsen number 0.00283 (according to Reynolds number 1415).

Unsteady subsonic, compressible, viscous, heat-conductive fluid flow past a confined square in a micro-channel – Mach number 0.1 and Knudsen number 0.00194 (according to Reynolds number 85) .

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Increasing velocity at the channel inflow from Mach number 2.43 to Mach number 4.86, for Knudsen number 0.05.

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Rayleigh-Bènard flow of a rarefied gas – the problem is defined in [1]

**Bibliography:**

1. K. Shterev and S. Stefanov, Pressure based finite volume method for calculation of compressible viscous gas flows, Journal of Computational Physics 229 (2010) pp. 461-480, doi:10.1016/j.jcp.2009.09.042 – the accepted manuscript can be downloaded from here, the paper in it`s final mode is available here.