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Volume 25, Issue 4
Multidimensional Relaxation Approximations for Hyperbolic Systems of Conservation Laws

Mohammed Seaïd

J. Comp. Math., 25 (2007), pp. 440-457.

Published online: 2007-08

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  • Abstract

We construct and implement a non-oscillatory relaxation scheme for multidimensional hyperbolic systems of conservation laws. The method transforms the nonlinear hyperbolic system to a semilinear model with a relaxation source term and linear characteristics which can be solved numerically without using either Riemann solver or linear iterations. To discretize the relaxation system we consider a high-resolution reconstruction in space and a TVD Runge-Kutta time integration. Detailed formulation of the scheme is given for problems in three space dimensions and numerical experiments are implemented in both scalar and system cases to show the effectiveness of the method.

  • Keywords

Multidimensional hyperbolic systems, Relaxation methods, Non-oscillatory reconstructions, Asymptotic-preserving schemes.

  • AMS Subject Headings

35L60, 35L65, 82B40, 65M20, 74S10, 65L06.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

seaid@mathematik.uni-kl.de (Mohammed Seaïd)

  • BibTex
  • RIS
  • TXT
@Article{JCM-25-440, author = {Seaïd , Mohammed}, title = {Multidimensional Relaxation Approximations for Hyperbolic Systems of Conservation Laws}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {4}, pages = {440--457}, abstract = {

We construct and implement a non-oscillatory relaxation scheme for multidimensional hyperbolic systems of conservation laws. The method transforms the nonlinear hyperbolic system to a semilinear model with a relaxation source term and linear characteristics which can be solved numerically without using either Riemann solver or linear iterations. To discretize the relaxation system we consider a high-resolution reconstruction in space and a TVD Runge-Kutta time integration. Detailed formulation of the scheme is given for problems in three space dimensions and numerical experiments are implemented in both scalar and system cases to show the effectiveness of the method.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8703.html} }
TY - JOUR T1 - Multidimensional Relaxation Approximations for Hyperbolic Systems of Conservation Laws AU - Seaïd , Mohammed JO - Journal of Computational Mathematics VL - 4 SP - 440 EP - 457 PY - 2007 DA - 2007/08 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8703.html KW - Multidimensional hyperbolic systems, Relaxation methods, Non-oscillatory reconstructions, Asymptotic-preserving schemes. AB -

We construct and implement a non-oscillatory relaxation scheme for multidimensional hyperbolic systems of conservation laws. The method transforms the nonlinear hyperbolic system to a semilinear model with a relaxation source term and linear characteristics which can be solved numerically without using either Riemann solver or linear iterations. To discretize the relaxation system we consider a high-resolution reconstruction in space and a TVD Runge-Kutta time integration. Detailed formulation of the scheme is given for problems in three space dimensions and numerical experiments are implemented in both scalar and system cases to show the effectiveness of the method.

Seaïd , Mohammed. (2007). Multidimensional Relaxation Approximations for Hyperbolic Systems of Conservation Laws. Journal of Computational Mathematics. 25 (4). 440-457. doi:
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