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

Mohammed Seaid

DOI:

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

Published online: 2007-08

Preview Full PDF 24 943
Export citation
  • 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
  • BibTex
  • RIS
  • TXT
@Article{JCM-25-440, author = {}, 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 JO - Journal of Computational Mathematics VL - 4 SP - 440 EP - 457 PY - 2007 DA - 2007/08 SN - 25 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/jcm/8703.html KW - Multidimensional hyperbolic systems KW - Relaxation methods KW - Non-oscillatory reconstructions KW - 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.
Mohammed Seaid. (1970). Multidimensional Relaxation Approximations for Hyperbolic Systems of Conservation Laws. Journal of Computational Mathematics. 25 (4). 440-457. doi:
Copy to clipboard
The citation has been copied to your clipboard