Asymptotically and exactly energy balanced augmented flux-ADER schemes with application to hyperbolic conservation laws with geometric source terms

Navas-Montilla, A. (Universidad de Zaragoza) ; Murillo, J. (Universidad de Zaragoza)

Resumen: In this work, an arbitrary order HLL-type numerical scheme is constructed using the flux-ADER methodology. The proposed scheme is based on an augmented Derivative Riemann solver that was used for the first time in Navas-Montilla and Murillo (2015) 1]. Such solver, hereafter referred to as Flux-Source (FS) solver, was conceived as a high order extension of the augmented Roe solver and led to the generation of a novel numerical scheme called AR-ADER scheme. Here, we provide a general definition of the FS solver independently of the Riemann solver used in it. Moreover, a simplified version of the solver, referred to as Linearized-Flux-Source (LFS) solver, is presented. This novel version of the FS solver allows to compute the solution without requiring reconstruction of derivatives of the fluxes, nevertheless some drawbacks are evidenced. In contrast to other previously defined Derivative Riemann solvers, the proposed FS and LFS solvers take into account the presence of the source term in the resolution of the Derivative Riemann Problem (DRP), which is of particular interest when dealing with geometric source terms. When applied to the shallow water equations, the proposed HLLS-ADER and AR-ADER schemes can be constructed to fulfill the exactly well-balanced property, showing that an arbitrary quadrature of the integral of the source inside the cell does not ensure energy balanced solutions. As a result of this work, energy balanced flux-ADER schemes that provide the exact solution for steady cases and that converge to the exact solution with arbitrary order for transient cases are constructed.

Idioma: Inglés

DOI: 10.1016/j.jcp.2016.04.047

Año: 2016

Publicado en: JOURNAL OF COMPUTATIONAL PHYSICS 317 (2016), 108-147
ISSN: 0021-9991

Factor impacto JCR: 2.744 (2016)

Categ. JCR: PHYSICS, MATHEMATICAL rank: 3 / 55 = 0.055 (2016) - Q1 - T1
Categ. JCR: COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS rank: 26 / 105 = 0.248 (2016) - Q1 - T1

Factor impacto SCIMAGO: 2.048 - Physics and Astronomy (miscellaneous) (Q1) - Computer Science Applications (Q1)

Tipo y forma: Artículo (PrePrint)

Área (Departamento): Área Mecánica de Fluidos (Dpto. Ciencia Tecnol.Mater.Fl.)