A numerical method for unsteady flows

Nicola Botta; Rolf Jeltsch

Applications of Mathematics (1995)

  • Volume: 40, Issue: 3, page 175-201
  • ISSN: 0862-7940

Abstract

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A high resolution finite volume method for the computation of unsteady solutions of the Euler equations in two space dimensions is presented and validated. The scheme is of Godunov-type. The first order part of the flux function uses the approximate Riemann problem solver of Pandolfi and here a new derivation of this solver is presented. This construction paves the way to understand the conditions under which the scheme satisfies an entropy condition. The extension to higher order is done by applying ideas of LeVeque to the approximate Riemann problem solution. A detailed validation of the scheme is done on one and two dimensional test problems.

How to cite

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Botta, Nicola, and Jeltsch, Rolf. "A numerical method for unsteady flows." Applications of Mathematics 40.3 (1995): 175-201. <http://eudml.org/doc/32915>.

@article{Botta1995,
abstract = {A high resolution finite volume method for the computation of unsteady solutions of the Euler equations in two space dimensions is presented and validated. The scheme is of Godunov-type. The first order part of the flux function uses the approximate Riemann problem solver of Pandolfi and here a new derivation of this solver is presented. This construction paves the way to understand the conditions under which the scheme satisfies an entropy condition. The extension to higher order is done by applying ideas of LeVeque to the approximate Riemann problem solution. A detailed validation of the scheme is done on one and two dimensional test problems.},
author = {Botta, Nicola, Jeltsch, Rolf},
journal = {Applications of Mathematics},
keywords = {finite volume method; Euler equations; Riemann problem; scheme of Godunov-type; high resolution finite volume method; Euler equations; Riemann problem solver; entropy condition},
language = {eng},
number = {3},
pages = {175-201},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A numerical method for unsteady flows},
url = {http://eudml.org/doc/32915},
volume = {40},
year = {1995},
}

TY - JOUR
AU - Botta, Nicola
AU - Jeltsch, Rolf
TI - A numerical method for unsteady flows
JO - Applications of Mathematics
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 40
IS - 3
SP - 175
EP - 201
AB - A high resolution finite volume method for the computation of unsteady solutions of the Euler equations in two space dimensions is presented and validated. The scheme is of Godunov-type. The first order part of the flux function uses the approximate Riemann problem solver of Pandolfi and here a new derivation of this solver is presented. This construction paves the way to understand the conditions under which the scheme satisfies an entropy condition. The extension to higher order is done by applying ideas of LeVeque to the approximate Riemann problem solution. A detailed validation of the scheme is done on one and two dimensional test problems.
LA - eng
KW - finite volume method; Euler equations; Riemann problem; scheme of Godunov-type; high resolution finite volume method; Euler equations; Riemann problem solver; entropy condition
UR - http://eudml.org/doc/32915
ER -

References

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  16. Some contributions to the modeling of discontinuous flows, Lecture Notes in Appl. Math. 22 (1985), 163–193. (1985) MR0818787
  17. The Riemann problem for two-dimensional gas dynamics and new limiters for high-order schemes, PhD thesis, Swiss Federal Institute of Technology, Diss. ETH No. 10297, 1993. (1993) MR1262404
  18. 10.1137/0705041, SIAM J. Numer. Anal. 5 (1968), 506–517. (1968) MR0235754DOI10.1137/0705041
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