Journal of Computational Physics
The effect of the earth pressure coefficients on the runout of granular material
Environmental Modelling & Software
On Well-Balanced Finite Volume Methods for Nonconservative Nonhomogeneous Hyperbolic Systems
SIAM Journal on Scientific Computing
Mathematical and Computer Modelling: An International Journal
Journal of Scientific Computing
Numerical Treatment of the Loss of Hyperbolicity of the Two-Layer Shallow-Water System
Journal of Scientific Computing
Hi-index | 31.45 |
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.