Publication detail

Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics

ZATOČILOVÁ, J. LUKÁČOVÁ, M.

English title

Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics

Type

Peer-reviewed article not indexed in WoS or Scopus

Language

en

Original abstract

In this paper we present recent results for the bicharacteristic based finite volume schemes, the so-called finite volume evolution Galerkin (FVEG) schemes. These methods were proposed to solve multi-dimensional hyperbolic conservation laws. They combine the usually conflicting design objectives of using the conservation form and following the characteristics, or bicharacteristics. This is realized by combining the finite volume formulation with approximate evolution operators, which use bicharacteristics of multi-dimensional hyperbolic system. In this way all of the infinitely many directions of wave propagation are taken into account. The main goal of this paper is to present a self contained overview on the recent results. We study the $L^1$-stability of the finite volume schemes obtained by different approximations of the flux integrals. Several numerical experiments presented in the last section confirm robustness and correct multi-dimensional behaviour of the FVEG methods.

Keywords in English

multidimensional finite volume methods, bicharacteristics, hyperbolic systems, wave equation, Euler equations

Released

2006-06-01

ISSN

0862-7940

Journal

Applications of Mathematics

Volume

51

Number

3

Pages from–to

205–228

Pages count

23

BIBTEX


@article{BUT88758,
  author="Jitka {Zatočilová} and Mária {Lukáčová}",
  title="Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics",
  journal="Applications of Mathematics",
  year="2006",
  volume="51",
  number="3",
  pages="205--228",
  issn="0862-7940"
}