Some examples of high order simulations parallel of inviscid flows on unstructured and hybrid meshes by residual distribution schemes

Abgrall, Rémi; Baurin, Guillaume; Jacq, Pascal; Ricchiuto, Mario

doi:10.1016/j.compfluid.2011.05.014

Cited by 5 publications

(2 citation statements)

References 13 publications

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“…The resulting scheme is referred to later on in the paper as LLFs (the first "L" for Limited, the "s" for stabilized). In [8] is discussed the choice of minimal quadrature formula for the evaluation of the integral term. Adding the least square term destroys in principle the maximum preserving property of the method, however in practice it does not, this is why we call this essentially non oscillatory RD scheme: the least square term acts as a mild filter of the spurious modes.…”

Section: Example Of Schemes and Conservationmentioning

confidence: 99%

Hyperbolic balance laws: residual distribution, local and global fluxes

Abgrall¹,

Ricchiuto²

2021

Preprint

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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 of 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.

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Section: Example Of Schemes and Conservationmentioning

confidence: 99%

Hyperbolic balance laws: residual distribution, local and global fluxes

Abgrall¹,

Ricchiuto²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…As in continuous and discontinuous finite element methods, the key toward high accuracy is the use of a high order polynomial representation of the unknowns in the computation of the cell residuals [4]. Although this approach has shown great potential in steady applications [2,3], the current state of the art [1] shows that further work is needed to bring the method to the level of maturity of more popular techniques, such as the discontinuous Galerkin (DG) method.…”

Section: • Residual Distribution Schemesmentioning

confidence: 99%