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.

An arbitrary high order and positivity preserving method for the shallow water equations / Ciallella, M.; Micalizzi, L.; Oeffner, P.; Torlo, D.. - In: COMPUTERS & FLUIDS. - ISSN 0045-7930. - 247:(2022). [10.1016/j.compfluid.2022.105630]

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

Torlo, D.
2022-01-01

Abstract

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.
2022
247
105630
https://arxiv.org/abs/2110.13509
Ciallella, M.; Micalizzi, L.; Oeffner, P.; Torlo, D.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/131392
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