The Formulation of Finite Difference Hermite RBF-WENO Schemes for Hyperbolic Conservation Laws: An Alternative Technique (Advances in Applied Mathematics and Mechanics, 2025)
A class of finite difference Hermite radial basis functions weighted essentially non-oscillatory (HRWENO) methods for solving conservation laws was presented by Abedian (Int. J. Numer. Meth. Fluids, 94 (2022), pp. 583–607). To reconstructthe fluxes in HRWENO, the common practice of reconstructing the flux functions wasemployed. In this follow-up research work, an alternative formulation to reconstructthe numerical fluxes is considered. First, the solution and its derivatives are directlyemployed to interpolate point values at interfaces of computational cells. Afterwards,the point values at interface of cell in building block are considered to obtain numerical fluxes. In this framework, arbitrary monotone fluxes can be employed, while inHRWENO the classical practice of reconstructing flux functions can be considered onlyto smooth flux splitting. Also, in the process of reconstruction these type of schemesconsider the effectively narrower stencil of HRWENO methods. Extensive test casessuch as Euler equations of compressible gas dynamics are considered to show the goodperformance of the methods.