  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.
