The Formulation of Finite Difference RBFWENO Schemes for Hyperbolic Conservation Laws: An Alternative Technique (Advances in Applied Mathematics and Mechanics, 2023)
To solve conservation laws, efficient schemes such as essentially non-oscillatory (ENO) and weighted ENO (WENO) have been introduced to control theGibbs oscillations. Based on radial basis functions (RBFs) with the classical WENO-JSweights, a new type of WENO schemes has been proposed to solve conservation laws[J. Guo et al., J. Sci. Comput., 70 (2017), pp. 551–575]. The purpose of this paper is tointroduce a new formulation of conservative finite difference RBFWENO schemes tosolve conservation laws. Unlike the usual method for reconstructing the flux functions,the flux function is generated directly with the conservative variables. Comparing withGuo and Jung (2017), the main advantage of this framework is that arbitrary monotonefluxes can be employed, while in Guo and Jung (2017) only smooth flux splitting canbe used to reconstruct flux functions. Several 1D and 2D benchmark problems areprepared to demonstrate the good performance of the new scheme.