Conservative logarithmic reconstructions and finite volume methods

Robert Artebrant; Achim Schroll

doi:10.1137/03060240X

Conservative logarithmic reconstructions and finite volume methods

Robert Artebrant, Achim Schroll

Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

Sammanfattning

A class of high-order reconstruction methods based on logarithmic functions is presented. Inspired by Marquina's hyperbolic method, we introduce a double logarithmic ansatz of fifth order of accuracy. Low variation is guaranteed by the ansatz and (slope-) limiting is avoided. The method can reconstruct smooth extrema without order reduction. Fifth order of convergence is verified in a numerical experiment governed by the nonlinear Euler system. Numerical experiments, including the Osher-Shu shock/acoustic interaction, are presented.

Originalspråk	engelska
Sidor (från-till)	294-314
Tidskrift	SIAM Journal on Scientific Computing
Volym	27
Nummer	1
DOI	https://doi.org/10.1137/03060240X
Status	Published - 2005

Bibliografisk information

The information about affiliations in this record was updated in December 2015.
The record was previously connected to the following departments: Numerical Analysis (011015004), Centre for Mathematical Sciences (011015000)

Ämnesklassifikation (UKÄ)

Matematik

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10.1137/03060240X

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title = "Conservative logarithmic reconstructions and finite volume methods",

abstract = "A class of high-order reconstruction methods based on logarithmic functions is presented. Inspired by Marquina's hyperbolic method, we introduce a double logarithmic ansatz of fifth order of accuracy. Low variation is guaranteed by the ansatz and (slope-) limiting is avoided. The method can reconstruct smooth extrema without order reduction. Fifth order of convergence is verified in a numerical experiment governed by the nonlinear Euler system. Numerical experiments, including the Osher-Shu shock/acoustic interaction, are presented.",

keywords = "high-order reconstruction, conservation law, finite volume method",

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AB - A class of high-order reconstruction methods based on logarithmic functions is presented. Inspired by Marquina's hyperbolic method, we introduce a double logarithmic ansatz of fifth order of accuracy. Low variation is guaranteed by the ansatz and (slope-) limiting is avoided. The method can reconstruct smooth extrema without order reduction. Fifth order of convergence is verified in a numerical experiment governed by the nonlinear Euler system. Numerical experiments, including the Osher-Shu shock/acoustic interaction, are presented.

KW - high-order reconstruction

KW - conservation law

KW - finite volume method

U2 - 10.1137/03060240X

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Conservative logarithmic reconstructions and finite volume methods

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