# On the connection between some Riemann-solver free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws

Tim Kröger; Sebastian Noelle; Susanne Zimmermann

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 38, Issue: 6, page 989-1009
- ISSN: 0764-583X

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topKröger, Tim, Noelle, Sebastian, and Zimmermann, Susanne. "On the connection between some Riemann-solver free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws." ESAIM: Mathematical Modelling and Numerical Analysis 38.6 (2010): 989-1009. <http://eudml.org/doc/194252>.

@article{Kröger2010,

abstract = {
In this paper, we present some interesting connections between a
number of Riemann-solver free approaches to the numerical solution
of multi-dimensional systems of conservation laws. As a main part,
we present a new and elementary derivation of Fey's Method of
Transport (MoT) (respectively the second author's ICE version of
the scheme) and the state decompositions which form the basis of it.
The only tools that we use are quadrature rules applied to the
moment integral used in the gas kinetic derivation of the Euler
equations from the Boltzmann equation, to the integration in time
along characteristics and to space integrals occurring in the finite
volume formulation. Thus, we establish a connection between the
MoT approach and the kinetic approach. Furthermore,
Ostkamp's equivalence result between her evolution Galerkin scheme
and the method of transport is lifted up from the level of
discretizations to the level of exact evolution operators,
introducing a new connection between the MoT and the
evolution Galerkin approach. At the same time, we clarify
some important differences between these two approaches.
},

author = {Kröger, Tim, Noelle, Sebastian, Zimmermann, Susanne},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Systems of conservation laws; Fey's method of transport;
Euler equations; Boltzmann equation; kinetic schemes;
bicharacteristic theory; state decompositions; flux decompositions;
exact and approximate integral representations; quadrature rules.; Galerkin method; method of transport; Euler equations},

language = {eng},

month = {3},

number = {6},

pages = {989-1009},

publisher = {EDP Sciences},

title = {On the connection between some Riemann-solver free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws},

url = {http://eudml.org/doc/194252},

volume = {38},

year = {2010},

}

TY - JOUR

AU - Kröger, Tim

AU - Noelle, Sebastian

AU - Zimmermann, Susanne

TI - On the connection between some Riemann-solver free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 38

IS - 6

SP - 989

EP - 1009

AB -
In this paper, we present some interesting connections between a
number of Riemann-solver free approaches to the numerical solution
of multi-dimensional systems of conservation laws. As a main part,
we present a new and elementary derivation of Fey's Method of
Transport (MoT) (respectively the second author's ICE version of
the scheme) and the state decompositions which form the basis of it.
The only tools that we use are quadrature rules applied to the
moment integral used in the gas kinetic derivation of the Euler
equations from the Boltzmann equation, to the integration in time
along characteristics and to space integrals occurring in the finite
volume formulation. Thus, we establish a connection between the
MoT approach and the kinetic approach. Furthermore,
Ostkamp's equivalence result between her evolution Galerkin scheme
and the method of transport is lifted up from the level of
discretizations to the level of exact evolution operators,
introducing a new connection between the MoT and the
evolution Galerkin approach. At the same time, we clarify
some important differences between these two approaches.

LA - eng

KW - Systems of conservation laws; Fey's method of transport;
Euler equations; Boltzmann equation; kinetic schemes;
bicharacteristic theory; state decompositions; flux decompositions;
exact and approximate integral representations; quadrature rules.; Galerkin method; method of transport; Euler equations

UR - http://eudml.org/doc/194252

ER -

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