A sub-cell WENO reconstruction method for spatial derivatives in the ADER scheme

  • Authors:

  • Jun Bo Cheng;Eleuterio F. Toro;Song Jiang;Weijun Tang

  • Affiliations:

  • -;-;-;-

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2013

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Abstract

We introduce a sub-cell WENO reconstruction method to evaluate spatial derivatives in the high-order ADER scheme. The basic idea in our reconstruction is to use only r stencils to reconstruct the point-wise values of solutions and spatial derivatives for the (2r-1)th-order ADER scheme in one dimension, while in two dimensions, the dimension-by-dimension sub-cell reconstruction approach for spatial derivatives is employed. Compared with the original ADER scheme of Toro and Titarev (2002) [2] that uses the direct derivatives of reconstructed polynomials for solutions to evaluate spatial derivatives, our method not only reduces greatly the computational costs of the ADER scheme on a given mesh, but also avoids possible numerical oscillations near discontinuities, as demonstrated by a number of one- and two-dimensional numerical tests. All these tests show that the 5th-order ADER scheme based on our sub-cell reconstruction method achieves the desired accuracy, and is essentially non-oscillatory and computationally cheaper for problems with discontinuities.