A particle-in-Burgers model: theory and numerics - Laboratoire de ...

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Model and motivation Auxiliary steps Results h = 0: coupling h = 0: definition, uniqueness h = 0: numerics, existence The coupled problem MAIN RESULTS
Model and motivation Auxiliary steps Results h = 0: coupling h = 0: definition, uniqueness h = 0: numerics, existence The coupled problem Main results: Auxiliary Problem 1 is well posed For the Burgers-with-Dirac-at-zero model , we apply the machinery developed for conservation laws with discontinuous flux (adapted entropies, Baiti,Jenssen and Audusse,Perthame ; revisited and generalized recently by BA., Karlsen, Risebro using the notion of admissibility germ ). The outcome is: – definition(s) of entropy solutions – uniqueness, continuous dependence (L 1 , L 1 loc dependence) exactly as in the Kruzhkov theory In addition, we find with domain of – a priori L ∞ bounds and (more delicate) variation bounds – a strikingly simple numerical method (monotone consistent finite volume scheme with a trick at the interface ) – convergence of the numerical scheme, existence . NB: the Riemann solver at the interface was already described by Lagoutière, Seguin, Takahashi , so a Godunov scheme could be constructed; but we seek to avoid using the Riemann solver because it is intricate.
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A particle-in-Burgers model: theory and numerics - Laboratoire de ...

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