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Article Dans Une Revue Computers and Fluids Année : 2022

An arbitrary high order and positivity preserving method for the shallow water equations

Résumé

In this paper, we develop and present an arbitrary high order well-balanced finite volume WENO method combined with the modified Patankar Deferred Correction (mPDeC) time integration method for the shallow water equations. Due to the positivity-preserving property of mPDeC, the resulting scheme is unconditionally positivity preserving for the water height. To apply the mPDeC approach, we have to interpret the spatial semi-discretization in terms of production-destruction systems. Only small modifications inside the classical WENO implementation are necessary and we explain how it can be done. In numerical simulations, focusing on a fifth order method, we demonstrate the good performance of the new method and verify the theoretical properties.
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Dates et versions

hal-03893632 , version 1 (11-12-2022)

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M. Ciallella, Lorenzo Micalizzi, Philipp Öffner, Davide Torlo. An arbitrary high order and positivity preserving method for the shallow water equations. Computers and Fluids, 2022, 247, pp.105630. ⟨10.1016/j.compfluid.2022.105630⟩. ⟨hal-03893632⟩
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