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Titarev V.A.,RAS Dorodnicyn Computing Center
International Journal of Heat and Mass Transfer | Year: 2012

The paper presents a numerical analysis of the nonlinear rarefied gas flow through a long planar channel of finite length. The solution is constructed for the arbitrary pressure and temperature drops, including flow into vacuum. The obtained results for the flow rates are compared with the linearized solutions in the large range of degree of gas rarefaction. The boundaries of the validity of the linearized approximation are established. © 2012 Elsevier Ltd. All rights reserved.

Titarev V.A.,RAS Dorodnicyn Computing Center
Vacuum | Year: 2013

The paper is devoted to the study of a rarefied gas flow through a circular pipe caused by small pressure differences between the reservoirs attached to the ends of the pipe. The analysis is based on of the direct numerical solution of the Boltzmann kinetic equation with the linearized model collision integral of Shakhov. The solution of the problem is computed for a wide range of the rarefaction parameter values and is compared with the kinetic and continuum solutions for an infinitely long circular pipe as well as with the flow into vacuum. © 2013 Elsevier Ltd. All rights reserved.

Titarev V.A.,RAS Dorodnicyn Computing Center
Communications in Computational Physics | Year: 2012

The paper is devoted to the development of an efficient deterministic framework for modelling of three-dimensional rarefied gas flows on the basis of the numerical solution of the Boltzmann kinetic equation with the model collision integrals. The framework consists of a high-order accurate implicit advection scheme on arbitrary unstructured meshes, the conservative procedure for the calculation of the model collision integral and efficient implementation on parallel machines. The main application area of the suggested methods is micro-scale flows. Performance of the proposed approach is demonstrated on a rarefied gas flow through the finite-length circular pipe. The results show good accuracy of the proposed algorithm across all flow regimes and its high efficiency and excellent parallel scalability for up to 512 cores. © 2012 Global-Science Press.

Azarova O.A.,RAS Dorodnicyn Computing Center
Aerospace Science and Technology | Year: 2015

The instabilities and vortices which arise as a result of an energy release effect on a shock layer produced by a blunt cylinder in a supersonic flow are considered. An energy deposition is supposed to have a shape of an infinite heated rarefied channel. The Richtmyer-Meshkov instability accompanied by the secondary instability is simulated inside a front separation area at Mach 1.9. The secondary Kelvin-Helmholtz instability is shown to be generated on the shear layers inside the density stratified vortex caused by the Richtmyer-Meshkov instability. Vortex drag reduction via the Richtmyer-Meshkov instability origination is discussed. The baroclinic nature of the vorticity production is established for the instabilities. Complex conservative difference schemes are used in the calculations. © 2015 Elsevier Masson SAS.

Shemyakova E.,RAS Dorodnicyn Computing Center
Programming and Computer Software | Year: 2012

The paper is devoted to the Darboux transformations, an effective algorithm for finding analytical solutions of partial differential equations. It is proved that Wronskian-like formulas suggested by G. Darboux for the second-order linear operators on the plane describe all possible differential transformations with M of the form D x + m(x, y) and D y + m(x, y), except for the Laplace transformations. © Pleiades Publishing, Ltd., 2012.

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