A Local Extrapolation Method for Hyperbolic Conservation Laws. I. The ENO Underlying Schemes

  • Authors:

  • Huanan Yang

  • Affiliations:

  • Department of Mathematics, Kansas State University, Manhattan, Kansas 66506

  • Venue:
  • Journal of Scientific Computing
  • Year:
  • 2000

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Abstract

In this paper, we introduce a local extrapolation method (LEM) for the essentially non-oscillatory (ENO) schemes solving nonlinear hyperbolic conservation laws. The method extrapolates the numerical flux of the underlying scheme so that it keeps conservativity. We use a minmod type limiter to avoid spurious oscillations. We propose a new balancing technique that preserves the symmetry of a symmetric wave that works well for a wide range of CFL numbers. We also introduce two artificial compression procedures to the LEM which yield sharp resolutions of contact discontinuities. Numerical examples are presented to illustrate the performance of the method.