Software Package \Nesvetay-3D" for modeling three-dimensional flows of monatomic rarefied gas

Nauka i Obrazovanie

V. A. Titarev¹ 

[1] Dorodnycin Computing Centre of RAS;

关键词: parallelism;    rarefied gas;    S-model;    kinetic equation;    implicit TVD method;   

DOI  :  10.7463/0614.0712314

来源: DOAJ

【 摘 要 】

Analysis of three-dimensional rarefied gas flowsin microdevices (micropipes, micropumps etc) and over re-entry vehicles requires development of methods of computational modelling. One of such methods is the direct numerical solution of the Boltzmann kinetic equation for the velocity distribution function with either exact or approximate (model) collision integral. At present, for flows of monatomic rarefied gas the Shakhov model kinetic equation, also called S-model, has gained wide-spread use. The equation can be regarded as a model equation of the incomplete thirdorder approximation. Despite its relative simplicity, the S-model is still a complicated integrodifferential equation of high dimension. The numerical solution of such an equation requires high-accuracy parallel methods.

The present work is a review of recent results concerning the development and application of three-dimensional computer package Nesvetay-3D intended for modelling of rarefied gas flows. The package solves Boltzmann kinetic equation with the BGK (Krook) and Shakhov model collision integrals using the discrete velocity approach. Calculations are carried out in non-dimensional variables. A finite integration domain and a mesh are introduced in the molecular velocity space. Next, the kinetic equation is re-written as a system of kinetic equations for each of the discrete velocities. The system is solved using an implicit finite-volume method of Godunov type. The steady-state solution is computed by a time marching method. High order of spatial accuracy is achieved by using a piece-wise linear representation of the distribution function in each spatial cell. In general, the coefficients of such an approximation are found using the least-square method. Arbitrary unstructured meshes in the physical space can be used in calculations, which allow considering flows over objects of general geometrical shape. Conservative property of the method with respect to the model collision integral is guaranteed by means of a special procedure to calculate macroscopic variables. Another important part of the numerical method is the fast solution of the linear system for time increments of the distribution function. The solution is based on the LU-SGS approach so that the number of operations is linearly proportional to the number of cells in the spatial mesh. Large problems can be solved on hundreds of CPU cores using the Message Passing Interface (MPI).

Performance and robustness of the numerical method and computer code are illustrated on a number of problems, including rarefied gas flows through microchannels into vacuum and external flows over re-entry vehicles on the high altitude of flight. Rarefied gas flows through simple and composite channels of circular cross sectional area are considered. Comparisons with the results of other authors and experimental data are shown.Good spatial mesh convergence of the method is demonstrated. For the flow in a composite channel the formation of a Mach disk is shown. One of the examples of external flow calculation is the analysis of rarefied gas flow over model winged re-entry space vehicle (RSV), which is a three-dimensional object of a very complex shape. The RSV is proposed by Central Aerohydrodynamic Institute (TsAGI). Its geometry includes a blunt fuselage, sweptwings, keel and flap. The flow pattern over the RSV and surface pressure distribution are shown.

At present the work is under way to incorporate an implicit numerical scheme for time-dependent rarefied gas flows, an adaptation algorithm for the efficient modelling of hypersonic flows over complex objects and extension to the diatomic gas modelling on the bases of the Rykov kinetic model.

【 授权许可】

Unknown