CIALLELLA, M.; MICALIZZI, Lorenzo; ÖFFNER, Philipp; TORLO, Davide

doi:10.1016/j.compfluid.2022.105630

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CIALLELLA, M.
Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]

MICALIZZI, Lorenzo
Universität Zürich [Zürich] = University of Zurich [UZH]

ÖFFNER, Philipp
Johannes Gutenberg - Universität Mainz = Johannes Gutenberg University [JGU]

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Computers and Fluids. 2022-10, vol. 247, p. 105630

Elsevier

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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.< Réduire

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positivity preserving

well-balanced

WENO

modified Patankar

shallow water

deferred correction

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

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