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Regularization of the Shock Wave Solution to the Riemann Problem for the Relativistic Burgers Equation

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  • Ting Zhang
  • Chun Shen

Abstract

The regularization of the shock wave solution to the Riemann problem for the relativistic Burgers equation is considered. For Riemann initial data consisting of a single decreasing jump, we find that the regularization of nonlinear convective term cannot capture the correct shock wave solution. In order to overcome it, we consider a new regularization technique called the observable divergence method introduced by Mohseni and discover that it can capture the correct shock wave solution. In addition, we take the Helmholtz filter for the fully explicit computation.

Suggested Citation

  • Ting Zhang & Chun Shen, 2014. "Regularization of the Shock Wave Solution to the Riemann Problem for the Relativistic Burgers Equation," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, August.
    • Handle: RePEc:hin:jnlaaa:178672
    DOI: 10.1155/2014/178672
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