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We consider an asymptotic preserving numerical scheme initially proposed by F. Filbet and S. Jin [229 (2010)] and G. Dimarco and L. Pareschi [49 (2011) 2057–2077] in the context of nonlinear and stiff kinetic equations. Here, we propose a convergence analysis of such a scheme for the approximation of a system of transport equations with a nonlinear source term, for which the asymptotic limit is given by a conservation law. We investigate the convergence of the approximate solution (
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This work aims to extend in two distinct directions results recently obtained in [10]. In a first step we focus on the possible extension of our results to the time
dependent case. Whereas in the second part some preliminary numerical simulations aim to
give orders of magnitudes in terms of numerical costs of direct 3D simulations.
We consider, in the first part, the time dependent rough problem for a simplified heat
equation in a straight channel that...
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