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

## TL;DR

This paper introduces a finite volume numerical scheme on unstructured grids for Savage-Hutter equations, effectively handling discontinuities and non-Galilean invariance, demonstrated through granular avalanche flow simulations.

## Contribution

A novel Godunov-type finite volume scheme with a modified HLL flux for Savage-Hutter equations on unstructured grids, addressing non-Galilean invariance and discontinuities.

## Key findings

- Scheme accurately captures shock waves in granular flows
- Numerical results agree well with reference solutions
- Applicable to complex avalanche simulations

## Abstract

A Godunov-type finite volume scheme on unstructured triangular grids is proposed to numerically solve the Savage-Hutter equations in curvilinear coordinate. We show the direct observation that the model is a not 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.