RT Journal Article
T1 High-order WENO finite-difference methods for hyperbolic nonconservative systems of partial differential equations
A1 Ren, Baifen
A1 Parés-Madroñal, Carlos María
K1 Matemáticas aplicadas
AB This work aims to extend the well-known high-order WENO finite-difference methods for systems of conservation laws to nonconservative hyperbolic systems. The main difficulty of these systems both from the theoretical and the numerical points of view comes from the fact that the definition of weak solution is not unique: according to the theory developed by Dal Maso, LeFloch, and Murat in 1995, it depends on the choice of a family of paths. A new strategy is introduced here that allows non-conservative products to be written as the derivative of a generalized flux function that is defined locally on the basis of the selected family of paths. WENO reconstructions are thenapplied to this generalized flux. Moreover, if a Roe linearization is available, the generalized flux function can be evaluated through matrix-vector operations instead of path-integrals. Two different known techniques are used to extend the methods to problems with source terms and the well-balanced properties of the resulting schemes are studied. These numerical schemes are applied to a coupled Burgers’ system and to the two-layer shallow water equations in one- and two- dimensions to obtain high-order methods that preserve water-at-rest steady states.
PB Elsevier
YR 2025
FD 2025-05-01
LK https://hdl.handle.net/10630/38658
UL https://hdl.handle.net/10630/38658
LA eng
NO Baifen Ren, Carlos Parés, High-order WENO finite-difference methods for hyperbolic nonconservative systems of partial differential equations, Journal of Computational Physics, Volume 535, 2025, 114047, ISSN 0021-9991, https://doi.org/10.1016/j.jcp.2025.114047.
NO Funding for open acces charge: Universidad de Málaga / CBUA
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 19 ene 2026