A finite element method for partially erodible bed evolution coupled with multiphase flows

Abstract

This paper introduces a continuous finite element model for two phase flows coupled with evolving bedforms. The method extends the positive definite non-oscillatory finite element algorithm (NFEM) capabilities to predict sediment transport, multiphase flow, and evolution of the resulting interfaces limiting fluids, erodible sediment layers and non-erodible strata. Free surface hydrodynamics is simulated by the integration of the governing equations for incompressible multiphase flows, including the advection and reinitialization of a phase function to update the interface location. Sign preservation of the algorithm is essential both for fluid interface tracking procedure and for the landform tracking. In the first case, the property avoids unphysical overshoots along the free surface. In the second case, a positive definite thickness of the erodible layer of sediment is mandatory to account for interaction between evolving cohesionless sediment layers and rigid beds. To compute sediment layer thickness, the method incorporates a conservation law to balance evolution of the bed position with sediment mass flux, including a general template for saturated flux calculation. The framework permits the simulation from bed load dominant transport to saltation dominant transport. Fluid/terrain interface is explicitly captured by a surface tracking methodology whereby the mesh is adapted to the bedform. Numerical experiments explore several saturated sediment flow formulae for interactive evolution of dune/atmosphere system, as well as stringent dam-break type problems on channels with dry beds and partially and totally erodible beds.