Fully and Semi-discrete Fourth-order Schemes for Hyperbolic Conservation Laws

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Abstract: A new fourth order accurate centered finite difference scheme for the solution of hyperbolic conservation laws is presented. A technique of making the fourth order scheme TVD is presented. The resulting scheme can avoid spurious oscillations and preserve fourth order accuracy in smooth parts. We discuss the extension of the TVD scheme to the nonlinear scalar hyperbolic conservation laws. For nonlinear systems, the TVD constraint is applied by solving shallow water equations. Then, we propose to use this fourth order flux as a building block in spatially fifth order weighted essentially non-oscillatory (WENO) schemes. The numerical solution is advanced in time by the third order TVD Runge — Kutta method. The performance of the scheme is assessed by solving test problems. The numerical results are presented and compared to the exact solutions and other methods.

Standort
Deutsche Nationalbibliothek Frankfurt am Main
Umfang
Online-Ressource
Sprache
Englisch

Erschienen in
Fully and Semi-discrete Fourth-order Schemes for Hyperbolic Conservation Laws ; volume:7 ; number:3 ; year:2007 ; pages:264-282
Computational methods in applied mathematics ; 7, Heft 3 (2007), 264-282

Urheber
Zahran, Y.H.

DOI
10.2478/cmam-2007-0017
URN
urn:nbn:de:101:1-2410261627597.282363243891
Rechteinformation
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
Letzte Aktualisierung
15.08.2025, 07:20 MESZ

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Beteiligte

  • Zahran, Y.H.

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