Asymptotic preserving scheme for a kinetic model describing incompressible fluids

Nicolas  Crouseilles; Mohammed  Lemou; SV Raghurama  Rao; Ankit  Ruhi; Muddu  Sekhar

doi:10.3934/krm.2016.9.51

Article Contents

2016, Volume 9, Issue 1: 51-74. Doi: 10.3934/krm.2016.9.51

This issue Previous Article Propagation of chaos for the spatially homogeneous Landau equation for Maxwellian molecules Next Article Global existence of weak solution to the free boundary problem for compressible Navier-Stokes

Asymptotic preserving scheme for a kinetic model describing incompressible fluids

1.
Inria Rennes Bretagne Atlantique (team IPSO) and IRMAR, University of Rennes 1, Campus de Beaulieu, 35042 Rennes
2.
CNRS and IRMAR, University of Rennes 1, Campus de Beaulieu, 35042 Rennes
3.
Department of Aerospace Engineering, Indian Institute of Science, Bangalore
4.
National Mathematics Initiative, Indian Institute of Science, Bangalore
5.
Department of Civil Engineering, Indian Institute of Science, Bangalore

Received: August 31, 2014

Revised: June 30, 2015

Published: February 2016

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Abstract

The kinetic theory of fluid turbulence modeling developed by Degond and Lemou in [7] 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 phenomenology, the relaxation time incorporates a dependency on the turbulent microscopic energy and this makes difficult the construction of efficient numerical methods. To investigate 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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Mathematics Subject Classification: 65M99, 65L04, 76B99, 76F05.

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