A High–Order WENO Scheme Based on Different Numerical Fluxes for the Savage–Hutter Equations

Min Wang and Xiaohua Zhang
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Min Wang: College of Civil Engineering & Architecture, China Three Gorges University, Yichang 443002, China
Xiaohua Zhang: Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, China

Mathematics, 2022, vol. 10, issue 9, 1-18

Abstract: The study of rapid free surface granular avalanche flows has attracted much attention in recent years, which is widely modeled using the Savage–Hutter equations. The model is closely related to shallow water equations. We employ a high-order shock-capturing numerical model based on the weighted essential non-oscillatory (WENO) reconstruction method for solving Savage–Hutter equations. Three numerical fluxes, i.e., Lax–Friedrichs (LF), Harten–Lax–van Leer (HLL), and HLL contact (HLLC) numerical fluxes, are considered with the WENO finite volume method and TVD Runge–Kutta time discretization for the Savage–Hutter equations. Numerical examples in 1D and 2D space are presented to compare the resolution of shock waves and free surface capture. The numerical results show that the method proposed provides excellent performance with high accuracy and robustness.

Keywords: granular avalanche flow; Savage–Hutter equations; WENO finite volume method; numerical flux (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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