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Solution to the Boltzmann kinetic equation for high-speed flows
Authors:F. G. Tcheremissine
Affiliation:(1) Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia
Abstract:The Boltzmann kinetic equation is solved by a finite-difference method on a fixed coordinate-velocity grid. The projection method is applied that was developed previously by the author for evaluating the Boltzmann collision integral. The method ensures that the mass, momentum, and energy conservation laws are strictly satisfied and that the collision integral vanishes in thermodynamic equilibrium. The last property prevents the emergence of the numerical error when the collision integral of the principal part of the solution is evaluated outside Knudsen layers or shock waves, which considerably improves the accuracy and efficiency of the method. The differential part is approximated by a second-order accurate explicit conservative scheme. The resulting system of difference equations is solved by applying symmetric splitting into collision relaxation and free molecular flow. The steady-state solution is found by the relaxation method.
Keywords:Boltzmann kinetic equation  rarefied gas  numerical methods  high-speed flows
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