Boltzmann schemes for continuum gas dynamics

Deshpande, S. M. (1993) Boltzmann schemes for continuum gas dynamics Sadhana (Academy Proceedings in Engineering Sciences), 18 (3-4). pp. 405-430. ISSN 0256-2499

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Many problems arising in the aerodynamic design of aerospace vehicles require the numerical solution of the Euler equations of gas dynamics. These are nonlinear partial differential equations admitting weak solutions such as shock waves and constructing robust numerical schemes for these equations is a challenging task. A new line of research called Boltzmann or kinetic schemes discussed in the present paper exploits the connection between the Boltzmann equation of the kinetic theory of gases and the Euler equations for inviscid compressible flows. Because of this connection, a suitable moment of a numerical scheme for the Boltzmann equation yields a numerical scheme for the Euler equations. This idea called the "moment method strategy" turns out to be an extremely rich methodology for developing robust numerical schemes for the Euler equations. The richness is demonstrated by developing a variety of kinetic schemes such as kinetic numerical method, kinetic flux vector splitting method, thermal velocity based splitting, multidirectional upwind method and least squares weak upwind scheme. A 3-D time-marching Euler code called Bheema based on the kinetic flux vector splitting method and its variants involving equilibrium chemistry have been developed for computing hypersonic reentry flows. The results obtained from the code Bheema demonstrate the robustness and the utility of the kinetic flux vector splitting method as a design tool in aerodynamics.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Boltzmann Equation; Kinetic Schemes for Euler Equation; Gas Dynamics; Computational Fluid Dynamics; Robust Numerical Schemes
ID Code:9471
Deposited On:02 Nov 2010 12:08
Last Modified:16 May 2016 19:16

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