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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	294-314
Journal	SIAM Journal on Scientific Computing
Volume	27
Issue number	1
DOIs	https://doi.org/10.1137/03060240X
Publication status	Published - 2005

Bibliographical note

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)

Subject classification (UKÄ)

Mathematics

Free keywords

high-order reconstruction
conservation law
finite volume method

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10.1137/03060240X

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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.",

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PY - 2005

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N2 - 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.

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.

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KW - conservation law

KW - finite volume method

U2 - 10.1137/03060240X

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M3 - Article

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JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

IS - 1

ER -

Conservative logarithmic reconstructions and finite volume methods

Abstract

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