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Asymptotic Preserving scheme for a kinetic model describing incompressible fluids

Abstract : The kinetic theory of fluid turbulence modeling developed by Degond and Lemou in [6] is considered for further study, analysis and simulation. Starting with the Boltzmann like equation representation for turbulence modeling, a relaxation type collision term is introduced for isotropic turbulence. In order to describe some important turbulence phe-nomenology, the relaxation time incorporates a dependency on the turbulent microscopic energy and this makes difficult the construction of efficient numerical methods. To investi-gate this problem, we focus here on a multi-dimensional prototype model and first propose an appropriate change of frame that makes the numerical study simpler. Then, a numerical strategy to tackle the stiff relaxation source term is introduced in the spirit of Asymptotic Preserving Schemes. Numerical tests are performed in a one-dimensional framework on the basis of the developed strategy to confirm its efficiency.
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https://hal.inria.fr/hal-01090677
Contributor : Nicolas Crouseilles <>
Submitted on : Thursday, December 4, 2014 - 6:41:42 AM
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Nicolas Crouseilles, Mohammed Lemou, S.V. Raghurama Rao, Ankit Ruhi, M. Sekhar. Asymptotic Preserving scheme for a kinetic model describing incompressible fluids. Kinetic and Related Models , AIMS, 2016, 9, pp.51-74. ⟨hal-01090677⟩

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