Preprint 2017-27
Antonio Baeza, Raimund Bürger, Pep Mulet, David Zorío:
Central WENO schemes through a global average weight
Abstract:
A novel central weighted essentially non-oscillatory (central WENO; CWENO)-type scheme for the construction of high-resolution approximations to discontinuous solutions to hyperbolic systems of conservation laws is presented. This procedure is based on the construction of a global average weight using the whole set of Jiang-Shu smoothness indicators associated to stencil. By this device one does not to have to rely on ideal weights, which, under certain stencil ar- rangements and interpolating point locations, do not de ne a convex combination of the interpolating lower-degree polynomials of the corresponding sub-stencils. Moreover, this procedure also prevents accuracy loss near smooth extrema. These properties result in a more exible scheme that overcomes these issues, at the cost of only few additional computations with respect to classical WENO schemes. Numerical examples illustrate the performance of the new CWENO schemes.
This preprint gave rise to the following definitive publication(s):
Antonio BAEZA, Raimund BüRGER, Pep MULET, David ZORíO: Central WENO schemes through a global average weight. Journal of Scientific Computing, vol. 78, 1, pp. 499-530, (2019).