Detail publikačního výsledku

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

ZATOČILOVÁ, J.; LUKÁČOVÁ, M.

Originální název

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

Anglický název

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

Druh

Článek recenzovaný mimo WoS a Scopus

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

ZATOČILOVÁ, J.; LUKÁČOVÁ, M.

Rok RIV

2013

Vydáno

01.06.2006

ISSN

0862-7940

Periodikum

Applications of Mathematics

Svazek

51

Číslo

3

Stát

Česká republika

Strany od

205

Strany do

228

Strany počet

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"
}