6533b851fe1ef96bd12aa055

RESEARCH PRODUCT

High Order in Space and Time Schemes Through an Approximate Lax-Wendroff Procedure

Antonio BaezaPep MuletDavid Zorío

subject

Discrete mathematicsSpacetimeLax–Wendroff methodSimple (abstract algebra)Scheme (mathematics)Finite differenceApplied mathematicsFluxClassification of discontinuitiesInterpolationMathematics

description

This paper deals with the scheme proposed by the authors in Zorio, Baeza and Mulet (J Sci Comput 71(1):246–273, 2017). This scheme is an alternative to the techniques proposed in Qiu and Shu (SIAM J Sci Comput 24(6):2185–2198, 2003) to obtain high-order accurate schemes using Weighted Essentially Non Oscillatory finite differences and approximating the flux derivatives required by the Cauchy-Kovalevskaya procedure by simple centered finite differences. We analyse how errors in first-order terms near discontinuities propagate through both versions of the Cauchy-Kovalevskaya procedure. We propose a fluctuation control, for which the approximation of the first-order derivative to be used in the Cauchy-Kovalevskaya procedure is obtained from a Weighted Essentially Non Oscillatory (WENO) interpolation of flux derivatives, instead of the usual finite difference of WENO flux reconstructions. The numerical results that we obtain confirm the benefits of this fluctuation control.

yearjournalcountryeditionlanguage
2017-01-01
https://doi.org/10.1007/978-3-319-65870-4_31