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

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