Local Total Variation Bounded Methods for Hyperbolic Conservation Laws

Article type: Research Article

Authors: Amat, Sergio^{a; 1; 2} | Busquier, Sonia^{a; 3} | Candela, Vicente^{b; 4; 5}

Affiliations: [a] Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Spain | [b] Departament de Matemàtica Aplicada, Universitat de València, Spain

Note: [1] Research supported in part by PI-53/00809/FS/01

Note: [2] E-mail: [email protected].

Note: [3] E-mail: [email protected].

Note: [4] E-mail: [email protected].

Note: [5] Research supported in part by DGICYT PB97-1402, in part by a grant from the Generalitat Valenciana and in part by ONR-N00014-95-1-0272.

Abstract: In this paper a family of local third order polynomic shock capturing methods for hyperbolic conservation laws is presented. We put out the fundamental aspects of original Piecewise Hyperbolic Method (PHM). Some numerical experiments are analyzed.

Keywords: Conservation laws, high order reconstruction, total variation

Keywords: 65M05, 65M10

DOI: 10.3233/JCM-2003-3302

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 3, no. 3, pp. 385-393, 2003