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High order residual distribution for steady state problems for hyperbolic conservation laws


Lin, Jianfang; Abgrall, Rémi; Qiu, Jianxian (2019). High order residual distribution for steady state problems for hyperbolic conservation laws. Journal of Scientific Computing, 79(2):891-913.

Abstract

In this paper, we propose a high order residual distribution conservative finite difference scheme for solving steady state conservation laws. A new type of WENO (weighted essentially non-oscillatory) termed as WENO-ZQ integration is used to compute the numerical fluxes and source term based on the point values of the solution, and the principles of residual distribution schemes are adapted to obtain steady state solutions. Extensive numerical examples in both scalar and system test problems in one and two dimensions demonstrate the efficiency, high order accuracy and the capability of resolving shocks of the proposed methods.

Abstract

In this paper, we propose a high order residual distribution conservative finite difference scheme for solving steady state conservation laws. A new type of WENO (weighted essentially non-oscillatory) termed as WENO-ZQ integration is used to compute the numerical fluxes and source term based on the point values of the solution, and the principles of residual distribution schemes are adapted to obtain steady state solutions. Extensive numerical examples in both scalar and system test problems in one and two dimensions demonstrate the efficiency, high order accuracy and the capability of resolving shocks of the proposed methods.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Theoretical Computer Science, General Engineering, Computational Theory and Mathematics, Software
Language:English
Date:1 May 2019
Deposited On:17 Jan 2019 07:47
Last Modified:17 Apr 2019 01:03
Publisher:Springer
ISSN:0885-7474
Additional Information:This is a post-peer-review, pre-copyedit version of an article published in Journal of Scientific Computing. The final authenticated version is available online at: https://doi.org/10.1007/s10915-018-0878-4
OA Status:Closed
Publisher DOI:https://doi.org/10.1007/s10915-018-0878-4

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Content: Accepted Version
Language: English
Filetype: PDF - Registered users only until 24 November 2019
Size: 605kB
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Embargo till: 2019-11-24