# 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

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topKurganov, 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

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

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