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.
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Sigal Gottlieb - The work of this author supported by NSF grant DMS-0106743.
Steven J. Ruuth - The work of this author was partially supported by a grant from NSERC Canada.
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Gottlieb, S., Mullen, J.S. & Ruuth, S.J. A Fifth Order Flux Implicit WENO Method. J Sci Comput 27, 271–287 (2006). https://doi.org/10.1007/s10915-005-9034-z
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DOI: https://doi.org/10.1007/s10915-005-9034-z