DOI QR코드

DOI QR Code

A NUMERICAL SCHEME WITH A MESH ON CHARACTERISTICS FOR THE CAUCHY PROBLEM FOR ONE-DIMENSIONAL HYPERBOLIC CONSERVATION LAWS

Yoon, Dae-Ki;Kim, Hong-Joong;Hwang, Woon-Jae

  • Published : 2009.07.31

Abstract

In this paper, a numerical scheme is introduced to solve the Cauchy problem for one-dimensional hyperbolic equations. The mesh points of the proposed scheme are distributed along characteristics so that the solution on the stencil can be easily and accurately computed. This is very important in reducing errors of the scheme because many numerical errors are generated when the solution is estimated over grid points. In addition, when characteristics intersect, the proposed scheme combines corresponding grid points into one and assigns new characteristic to the point in order to improve computational efficiency. Numerical experiments on the inviscid Burgers' equation have been presented.

Keywords

conservation laws;moving mesh;non-oscillatory scheme

References

  1. G. Capdeville, A hermite upwind weno scheme for solving hyperbolic conservation laws, J. Comput. Phys. 227 (2008), 2430–2454 https://doi.org/10.1016/j.jcp.2007.10.017
  2. W. Huang, Y. Ren, and R. Russel, Moving mesh partial differential equations (mmpdes) based on the equidistribution principle, SIAM J. Numer. Anal. 31 (1994), 709–730 https://doi.org/10.1137/0731038
  3. R. J. LeVeque, Numerical methods for conservation laws, Birkhauser, 1992
  4. R. M. M. Mattheij, S. W. Rienstra, and J. H. M. ten Thije Boonkkamp, Partial differential equations, modeling, analysis, computation, SIAM, 2005
  5. Y. Di, R. Li, T. Tang, and P. Zhang, Moving mesh finite element methods for the incompressible navier-stokes equations, SIAM J. Sci. Comput. 26 (2005), no. 3, 1036–1056 https://doi.org/10.1137/030600643
  6. G. Jiang and C. W. Shu, Efficient implementation of weighted eno schemes, J. Comput. Phys. 126 (1996), 202–228 https://doi.org/10.1006/jcph.1996.0130
  7. D. Kim and J. H. Kwon, A high-order accurate hybrid scheme using a central flux scheme and a weno scheme for compressible flow field analysis, J. Comput. Phys. 210 (2005), 554–583 https://doi.org/10.1016/j.jcp.2005.04.023