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A MOOD-MUSCL Hybrid Formulation for the Non-conservative Shallow-Water System

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Abstract

The stability of the high-order finite volume method for hyperbolic systems is based on non-linear procedures that prevent the creation of non-physical oscillations. Traditional techniques use the a priori paradigm where the procedure is carried out with the current time step solution. The a posteriori paradigm lies on an advanced in time candidate solution and a posterior evaluation of its stability, followed by a cure when necessary. To compare the two strategies, we propose a detailed study using the non-conservative shallow-water equations as a prototype, where both techniques are applied together in the framework of second-order linear reconstruction for the sake of simplicity. Then, a hybrid version combining the most positive aspects of both methods is proposed and analysed.

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Acknowledgements

The authors acknowledge the financial support by FEDER – Fundo Europeu de Desenvolvimento Regional, through COMPETE 2020 – Programa Operacional Fatores de Competitividade, and the National Funds through FCT – Fundação para a Ciência e a Tecnologia, Project No. POCI-01-0145-FEDER-028118, PTDC/MAT-APL/28118/2017. This work was partially financially supported by: Project POCI-01-0145-FEDER-028247 - funded by FEDER funds through COMPETE2020 - Programa Operacional Competitividade e Internacionalização (POCI) and by national funds (PIDDAC) through FCT/MCTES. This work was supported by the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Funding UIDB/04650/2020.

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  1. Centre of Physics and Department of Mathematics, University of Minho, Campus de Gualtar, 4710-057, Braga, Portugal

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Figueiredo, J., Clain, S. A MOOD-MUSCL Hybrid Formulation for the Non-conservative Shallow-Water System. J Sci Comput 88, 2 (2021). https://doi.org/10.1007/s10915-021-01513-z

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