A Finite Volume Scheme for Savage-Hutter Equations on Unstructured Grids

Ruo Li 1 and Xiaohua Zhang 2,∗

1 CAPT, LMAM and School of Mathematical Sciences, Peking University,

Beijing 100871, China

2 College of Science and Three Gorges Mathematical Research Center, China

Three Gorges University, Yichang, Hubei 443002, China

Abstract.

A Godunov-type finite volume scheme on unstructured grids is proposed to numerically solve the Savage-Hutter equations in curvilinear coordinate. We show the direct observation that the model isn’t a Galilean invariant system. At the cell boundary, the modified Harten-Lax-van Leer (HLL) approximate Riemann solver is adopted to calculate the numerical flux. The modified HLL flux is not troubled by the

lack of Galilean invariance of the model and it is helpful to handle discontinuities at free interface. Rigidly the system is not always a hyperbolic system due to the dependence of flux on the velocity gradient. Even though, our numerical results still show quite good agreements to reference solutions. The simulations for granular avalanche flows with shock waves indicate that the scheme is applicable.

AMS subject classifications: 65M10, 65M15, 65N30

Key words: Granular avalanche flow, Savage-Hutter equations, finite volume method, Galilean invariant.