Central schemes and contact discontinuities

Alexander Kurganov; Guergana Petrova

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 6, page 1259-1275
  • ISSN: 0764-583X

Abstract

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We introduce a family of new second-order Godunov-type central schemes for one-dimensional systems of conservation laws. They are a less dissipative generalization of the central-upwind schemes, proposed in [A. Kurganov et al., submitted to SIAM J. Sci. Comput.], whose construction is based on the maximal one-sided local speeds of propagation. We also present a recipe, which helps to improve the resolution of contact waves. This is achieved by using the partial characteristic decomposition, suggested by Nessyahu and Tadmor [J. Comput. Phys.87 (1990) 408-463], which is efficiently applied in the context of the new schemes. The method is tested on the one-dimensional Euler equations, subject to different initial data, and the results are compared to the numerical solutions, computed by other second-order central schemes. The numerical experiments clearly illustrate the advantages of the proposed technique.

How to cite

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Kurganov, Alexander, and Petrova, Guergana. "Central schemes and contact discontinuities." ESAIM: Mathematical Modelling and Numerical Analysis 34.6 (2010): 1259-1275. <http://eudml.org/doc/197505>.

@article{Kurganov2010,
abstract = { We introduce a family of new second-order Godunov-type central schemes for one-dimensional systems of conservation laws. They are a less dissipative generalization of the central-upwind schemes, proposed in [A. Kurganov et al., submitted to SIAM J. Sci. Comput.], whose construction is based on the maximal one-sided local speeds of propagation. We also present a recipe, which helps to improve the resolution of contact waves. This is achieved by using the partial characteristic decomposition, suggested by Nessyahu and Tadmor [J. Comput. Phys.87 (1990) 408-463], which is efficiently applied in the context of the new schemes. The method is tested on the one-dimensional Euler equations, subject to different initial data, and the results are compared to the numerical solutions, computed by other second-order central schemes. The numerical experiments clearly illustrate the advantages of the proposed technique. },
author = {Kurganov, Alexander, Petrova, Guergana},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Euler equations of gas dynamics; partial characteristic decomposition; fully-discrete and semi-discrete central schemes.; conservation laws; contact discontinuities; high-resolution methods; central schemes; numerical examples; Euler equations},
language = {eng},
month = {3},
number = {6},
pages = {1259-1275},
publisher = {EDP Sciences},
title = {Central schemes and contact discontinuities},
url = {http://eudml.org/doc/197505},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Kurganov, Alexander
AU - Petrova, Guergana
TI - Central schemes and contact discontinuities
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 6
SP - 1259
EP - 1275
AB - We introduce a family of new second-order Godunov-type central schemes for one-dimensional systems of conservation laws. They are a less dissipative generalization of the central-upwind schemes, proposed in [A. Kurganov et al., submitted to SIAM J. Sci. Comput.], whose construction is based on the maximal one-sided local speeds of propagation. We also present a recipe, which helps to improve the resolution of contact waves. This is achieved by using the partial characteristic decomposition, suggested by Nessyahu and Tadmor [J. Comput. Phys.87 (1990) 408-463], which is efficiently applied in the context of the new schemes. The method is tested on the one-dimensional Euler equations, subject to different initial data, and the results are compared to the numerical solutions, computed by other second-order central schemes. The numerical experiments clearly illustrate the advantages of the proposed technique.
LA - eng
KW - Euler equations of gas dynamics; partial characteristic decomposition; fully-discrete and semi-discrete central schemes.; conservation laws; contact discontinuities; high-resolution methods; central schemes; numerical examples; Euler equations
UR - http://eudml.org/doc/197505
ER -

References

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Citations in EuDML Documents

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  1. Smadar Karni, Eduard Kirr, Alexander Kurganov, Guergana Petrova, Compressible two-phase flows by central and upwind schemes
  2. Smadar Karni, Eduard Kirr, Alexander Kurganov, Guergana Petrova, Compressible two-phase flows by central and upwind schemes
  3. Alina Chertock, Alexander Kurganov, On a hybrid finite-volume-particle method
  4. Alexander Kurganov, Doron Levy, Central-upwind schemes for the Saint-Venant system
  5. Alexander Kurganov, Doron Levy, Central-Upwind Schemes for the Saint-Venant System
  6. Alina Chertock, Alexander Kurganov, On a hybrid finite-volume-particle method

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