# A hybrid scheme to compute contact discontinuities in one-dimensional Euler systems

Thierry Gallouët; Jean-Marc Hérard; Nicolas Seguin

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 36, Issue: 6, page 1133-1159
- ISSN: 0764-583X

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topGallouët, Thierry, Hérard, Jean-Marc, and Seguin, Nicolas. "A hybrid scheme to compute contact discontinuities in one-dimensional Euler systems." ESAIM: Mathematical Modelling and Numerical Analysis 36.6 (2010): 1133-1159. <http://eudml.org/doc/194143>.

@article{Gallouët2010,

abstract = {
The present paper is devoted to the computation of single phase or
two phase flows using the single-fluid approach. Governing equations
rely on Euler equations which may be supplemented by conservation
laws for mass species. Emphasis is given on numerical modelling
with help of Godunov scheme or an approximate form of Godunov scheme
called VFRoe-ncv based on velocity and pressure variables. Three
distinct classes of closure laws to express the internal energy in
terms of pressure, density and additional variables are exhibited.
It is shown first that a standard conservative formulation of above
mentioned schemes enables to predict “perfectly” unsteady contact
discontinuities on coarse meshes, when the equation of state (EOS)
belongs to the first class. On the basis of previous work issuing
from literature, an almost conservative though modified version of
the scheme is proposed to deal with EOS in the second or third
class. Numerical evidence shows that the accuracy of approximations
of discontinuous solutions of standard Riemann problems is
strengthened on coarse meshes, but that convergence towards the
right shock solution may be lost in some cases involving complex EOS
in the third class. Hence, a blend scheme is eventually proposed to
benefit from both properties (“perfect” representation of contact
discontinuities on coarse meshes, and correct convergence on finer
meshes). Computational results based on an approximate Godunov
scheme are provided and discussed.
},

author = {Gallouët, Thierry, Hérard, Jean-Marc, Seguin, Nicolas},

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

keywords = {Godunov scheme; Euler system; contact discontinuities;
thermodynamics; conservative schemes.; thermodynamics; conservative schemes},

language = {eng},

month = {3},

number = {6},

pages = {1133-1159},

publisher = {EDP Sciences},

title = {A hybrid scheme to compute contact discontinuities in one-dimensional Euler systems},

url = {http://eudml.org/doc/194143},

volume = {36},

year = {2010},

}

TY - JOUR

AU - Gallouët, Thierry

AU - Hérard, Jean-Marc

AU - Seguin, Nicolas

TI - A hybrid scheme to compute contact discontinuities in one-dimensional Euler systems

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 36

IS - 6

SP - 1133

EP - 1159

AB -
The present paper is devoted to the computation of single phase or
two phase flows using the single-fluid approach. Governing equations
rely on Euler equations which may be supplemented by conservation
laws for mass species. Emphasis is given on numerical modelling
with help of Godunov scheme or an approximate form of Godunov scheme
called VFRoe-ncv based on velocity and pressure variables. Three
distinct classes of closure laws to express the internal energy in
terms of pressure, density and additional variables are exhibited.
It is shown first that a standard conservative formulation of above
mentioned schemes enables to predict “perfectly” unsteady contact
discontinuities on coarse meshes, when the equation of state (EOS)
belongs to the first class. On the basis of previous work issuing
from literature, an almost conservative though modified version of
the scheme is proposed to deal with EOS in the second or third
class. Numerical evidence shows that the accuracy of approximations
of discontinuous solutions of standard Riemann problems is
strengthened on coarse meshes, but that convergence towards the
right shock solution may be lost in some cases involving complex EOS
in the third class. Hence, a blend scheme is eventually proposed to
benefit from both properties (“perfect” representation of contact
discontinuities on coarse meshes, and correct convergence on finer
meshes). Computational results based on an approximate Godunov
scheme are provided and discussed.

LA - eng

KW - Godunov scheme; Euler system; contact discontinuities;
thermodynamics; conservative schemes.; thermodynamics; conservative schemes

UR - http://eudml.org/doc/194143

ER -

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