A Fifth Order Flux Implicit WENO Method

Authors:
Sigal Gottlieb;Julia S. Mullen;Steven J. Ruuth
Affiliations:
Department of Mathematics, UMASS-Dartmouth North Dartmouth, MA and Division of Applied Mathematics, Brown University, Providence, USA;Worcester Polytechnic Institute, Worcester, USA;Department of Mathematics, Simon Fraser University, Burnaby, Canada V5A 1S6
Venue:
Journal of Scientific Computing
Year:
2006

Citing 6
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Abstract

The weighted essentially non-oscillatory (WENO) method is an excellent spatial discretization for hyperbolic partial differential equations with discontinuous solutions. However, the time-step restriction associated with explicit methods may pose severe limitations on their use in applications requiring large scale computations. An efficient implicit WENO method is necessary. In this paper, we propose a prototype flux-implicit WENO (iWENO) method. Numerical tests on classical scalar equations show that this is a viable and stable method, which requires appropriate time-stepping methods. Future study will include the examination of such methods as well as extension of iWENO to systems and higher dimensional problems.