Open AccessA Runge-Kutta discontinuous Galerkin solver for 2D Boltzmann model equations: Verification and analysis of computational performance
Author(s) -
Wei Su,
Alina Alexeenko,
Guobiao Cai
Publication year - 2012
Publication title -
aip conference proceedings
Language(s) - English
Resource type - Conference proceedings
SCImago Journal Rank - 0.177
H-Index - 75
eISSN - 1551-7616
pISSN - 0094-243X
DOI - 10.1063/1.4769547
Subject(s) - discontinuous galerkin method , discretization , boltzmann equation , runge–kutta methods , solver , finite volume method , mathematics , relaxation (psychology) , momentum (technical analysis) , conservation law , thermal conduction , boltzmann constant , mathematical analysis , physics , mathematical optimization , finite element method , numerical analysis , mechanics , psychology , social psychology , finance , economics , thermodynamics , quantum mechanics
The high-order Runge-Kutta discontinuous Galerkin (DG) method is extended to the 2D kinetic model equations describing rarefied gas flows. A DG-type discretization of the equilibrium velocity distributions is formulated for the Bhatnagar-Gross-Krook and ellipsoidal statistical models which enforce a weak conservation of mass, momentum and energy in the collision relaxation term. The RKDG solutions have up to 3rd-order spatial accuracy and up to 4 th-order time accuracy. Verification is carried out for a steady 1D Couette flow and a 2D thermal conduction problem by comparison with DSMC and analytical solutions. The computational performance of the RKDG method is compared with a widely used second-order finite volume method. © 2012 American Institute of Physics.
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