Asymptotic preserving scheme for a kinetic model describing incompressible fluids
Nicolas Crouseilles - Inria Rennes Bretagne Atlantique (team IPSO) and IRMAR, University of Rennes 1, Campus de Beaulieu, 35042 Rennes, France (email)
Abstract: The kinetic theory of fluid turbulence modeling developed by Degond and Lemou in  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.
Received: September 2014; Revised: July 2015; Available Online: October 2015.
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