High-resolution finite compact difference schemes for hyperbolic conservation laws

  • Authors:

  • Yiqing Shen;Guowei Yang;Zhi Gao

  • Affiliations:

  • LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing, PR China;LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing, PR China;LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing, PR China

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2006

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Abstract

A finite compact (FC) difference scheme requiring only bi-diagonal matrix inversion is proposed by using the known high-resolution flux. Introducing TVD or ENO limiters in the numerical flux, several high-resolution FC-schemes of hyperbolic conservation law are developed, including the FC-TVD, third-order FC-ENO and fifth-order FC-ENO schemes. Boundary conditions formulated need only one unknown variable for third-order FC-ENO scheme and two unknown variables for fifth-order FC-ENO scheme. Numerical test results of the proposed FC-scheme were compared with traditional TVD, ENO and WENO schemes to demonstrate its high-order accuracy and high-resolution.