A new Savage-Hutter type model for submarine avalanches and generated tsunami

Abstract

In this paper we present a new two-layer model of Savage-Hutter type to study submarine avalanches. A layer composed of fluidized granular material is assumed to flow within an upper layer composed of an inviscid fluid (e. g. water). The model is derived in a system of local coordinates following a non-erodible bottom and takes into account its curvature. We prove that the model verifies an entropy inequality, preserves water at rest for a sediment layer and their solutions can be seen as particular solutions of incompressible Euler equations under hydrostatic assumptions. Buoyancy effects and the centripetal acceleration of the grain movement due to the curvature of the bottom are considered in the definition of the Coulomb term. We propose a two-step Roe type solver to discretize the presented model. It exactly preserves water at rest and no movement of the sediment layer, when its angle is smaller than the angle of repose, and up to second order all stationary solutions. Finally, some numerical tests are performed by simulating submarine and sub-aerial avalanches as well as the generated tsunami.