A visual fluctuation splitting scheme for magnetohydrodynamics with a new sonic fix and Euler limit

Aslan, Necdet

doi:10.1016/j.jcp.2003.11.029

“…(1), dimensionless forms are obtained with the following relationships between the normalizing parameters:…”

Section: Dimensionless Formsmentioning

confidence: 99%

“…Note that several wave models have been developed for the Euler equations [5] and for the MHD equations [1,4]. As done with other wave models, ION-A is utilized to calculate the individual fluctuations of possible waves, by first determining their effects due to the gradients in the physical variables, and then distributing them to the nodes of triangles in an upwind manner.…”

Section: Numerical Solution Proceduresmentioning

confidence: 99%

“…(24), and the conservative eigenvectors, r u using the matrix: oU/oW, 7. having determined the eigen-system of 6 individual waves for each wave, k 7.1. get the wave fluctuation from Eq. (19) using the averaged values: k k ; a k and r k u , 7.2. using the mesh properties andñðhÞ ¼ ðcos h; sin hÞ, determine the upwind nodes for this wave and assign U k to these nodes of T using the distribution technique described in [1] or [5].…”

Section: Solution Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

A numerical scheme for ionizing shock waves

Aslan

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Mond

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2005

Journal of Computational Physics

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Residual Distribution Schemes: Foundations and Analysis

Deconinck¹,

Ricchiuto²

2004

Encyclopedia of Computational Mechanics

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In this article, we introduce and analyze the class of numerical schemes known as residual distribution or fluctuation splitting schemes. The root of this family of discretizations is found mainly in works aiming at generalizing the finite volume techniques to a genuinely multidimensional upwinding context, as in, for example (Hall, Morton, Ni, Roe). However, the final result is a numerical method sharing a lot with other techniques, such as finite element schemes (Carette, Deconinck, Paillere and Roe, 1995). Our aim is to look at fluctuation splitting/residual distribution methods from a generic theoretical point of view. We discuss in a general way the basic principles and the criteria used in the design of the schemes: positivity, k‐exacteness, energy stability, well‐balancedness. We also show similarities with known, more classical, discretization techniques, as well as the main distinguishing features that make residual distribution methods a valid alternative to these classical schemes. Finally, we present some numerical applications and comparisons. Throughout the text, we give an extensive overview of the existing literature, and finally conclude the chapter by reviewing most of the ongoing research on the topic.

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Residual Distribution Schemes: Foundations and Analysis

Deconinck

¹

,

Ricchiuto

²

2017

Encyclopedia of Computational Mechanics Second Edition

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In this article, we introduce and analyze the class of numerical schemes known as residual distribution or fluctuation splitting schemes. The root of this family of discretizations is found mainly in works aiming at generalizing the finite volume techniques to a genuinely multidimensional upwinding context, as in, for example (Hall, Morton, Ni, Roe). However, the final result is a numerical method sharing a lot with other techniques, such as finite element schemes (Carette, Deconinck, Paillere and Roe, 1995). Our aim is to look at fluctuation splitting/residual distribution methods from a generic theoretical point of view. We discuss in a general way the basic principles and the criteria used in the design of the schemes: positivity, k‐exacteness, energy stability, well‐balancedness. We also show similarities with known, more classical, discretization techniques, as well as the main distinguishing features that make residual distribution methods a valid alternative to these classical schemes. Finally, we present some numerical applications and comparisons. Throughout the text, we give an extensive overview of the existing literature, and finally conclude the chapter by reviewing most of the ongoing research on the topic.

show abstract

A visual fluctuation splitting scheme for magnetohydrodynamics with a new sonic fix and Euler limit

Cited by 6 publications

References 33 publications

A numerical scheme for ionizing shock waves

A numerical scheme for ionizing shock waves

Residual Distribution Schemes: Foundations and Analysis

Residual Distribution Schemes: Foundations and Analysis

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