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Séminaire de Calcul Scientifique et Modélisation

Numerical schemes for the equation of the BGK model

Gabriella Puppo

( Politecnico di Torino )

Salle 1

le 14 février 2013 à 11:00

I will describe a class of numerical methods for the BGK model of kinetic equations. The schemes proposed are implicit with respect to the distribution function, while the macroscopic moments are evolved explicitly. In this fashion, the stability condition on the time step coincides with a macroscopic CFL, evaluated using estimated values for the macroscopic velocity and sound speed. Thus the stability restriction does not depend on the relaxation time and it does not depend on the microscopic velocity of energetic particles either. With the technique proposed here, the updating of the distribution function requires the solution of a linear system of equations, even though the BGK model is highly non linear. Thus the proposed schemes are particularly effectiveclose to the hydrodynamic regime, where the macroscopic CFL condition is comparable to accuracy requirements. We prove the asymptotic preserving (AP) properties of the method, and we show that thsi technique has a stabilizing effect in the Navier Stokes regime. We show results for schemes of order 1 and 2, and the generalization to higher order is sketched.