ABGRALL, Rémi; RICCHIUTO, Mario

doi:10.1007/978-981-16-9665-7_7

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ABGRALL, Rémi
Universität Zürich [Zürich] = University of Zurich [UZH]

RICCHIUTO, Mario
Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]

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Numerical Fluid Dynamics, Numerical Fluid Dynamics. 2022-05-19p. 177-222

Springer Nature Singapore

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This review paper describes a class of scheme named “residual distribution schemes” or “fluctuation splitting schemes”. They are a generalization of Roe’s numerical flux [61] in fluctuation form. The so-called multidimensional fluctuation schemes have historically first been developed for steady homogeneous hyperbolic systems. Their application to unsteady problems and conservation laws has been really understood only relatively recently. This understanding has allowed to make the residual distribution framework a powerful playground to develop numerical discretizations embedding some prescribed constraints. This paper describes in some detail these techniques, with several examples, ranging from the compressible Euler equations to the Shallow Water equations.< Réduire

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Hyperbolic Balance Laws: Residual Distribution, Local and Global Fluxes

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