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ZATOČILOVÁ, J. LUKÁČOVÁ, M.
Original Title
Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics
Type
journal article - other
Language
English
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
multidimensional finite volume methods, bicharacteristics, hyperbolic systems, wave equation, Euler equations
Authors
ZATOČILOVÁ, J.; LUKÁČOVÁ, M.
Released
1. 6. 2006
ISBN
0862-7940
Periodical
APPLICATIONS OF MATHEMATICS
Year of study
51
Number
3
State
Czech Republic
Pages from
205
Pages to
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" }