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1 LJLL - Laboratoire Jacques-Louis Lions 2 MAMBA - Modelling and Analysis for Medical and Biological Applications LJLL - Laboratoire Jacques-Louis Lions, Inria de Paris 3 Shanghai Jiao Tong University Shanghai

Abstract : In this paper, we propose a general framework for designing numerical schemes that have both well-balanced WB and asymptotic preserving AP properties, for various kinds of kinetic models. We are interested in two different parameter regimes, 1 When the ratio between the mean free path and the characteristic macroscopic length ε tends to zero, the density can be described by advection diffusion type linear or nonlinear macroscopic models; 2 When ε = O1, the models behave like hyperbolic equations with source terms and we are interested in their steady states. We apply the framework to three different kinetic models: neutron transport equation and its diffusion limit, the transport equation for chemotaxis and its Keller-Segel limit, and grey radiative transfer equation and its nonlinear diffusion limit. Numerical examples are given to demonstrate the properties of the schemes.

Keywords : Kinetic models well-balanced asymptotic preserving





Author: Casimir Emako - Min Tang -

Source: https://hal.archives-ouvertes.fr/



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