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Kinetic and Related Models (KRM)
 

Asymptotic preserving scheme for a kinetic model describing incompressible fluids

Pages: 51 - 74, Volume 9, Issue 1, March 2016      doi:10.3934/krm.2016.9.51

 
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Nicolas Crouseilles - Inria Rennes Bretagne Atlantique (team IPSO) and IRMAR, University of Rennes 1, Campus de Beaulieu, 35042 Rennes, France (email)
Mohammed Lemou - CNRS and IRMAR, University of Rennes 1, Campus de Beaulieu, 35042 Rennes, France (email)
SV Raghurama Rao - Department of Aerospace Engineering, Indian Institute of Science, Bangalore, India (email)
Ankit Ruhi - National Mathematics Initiative, Indian Institute of Science, Bangalore, India (email)
Muddu Sekhar - Department of Civil Engineering, Indian Institute of Science, Bangalore, India (email)

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.

Keywords:  Asymptotic preserving methods, incompressible flow, change of frame, stiff source terms, numerical simulation, kinetic turbulence model.
Mathematics Subject Classification:  65M99, 65L04, 76B99, 76F05.

Received: September 2014;      Revised: July 2015;      Available Online: October 2015.

 References