Layer-averaged modeling of two-dimensional turbidity currents with a dissipative-Galerkin finite element method Part I: Formulation and application example

A finite element technique has been applied to the layer-averaged equations describing a turbidity current which propagates two-dimensionally in deep ambient water. The governing equations form a hyperbolic system of partial differential equations, namely continuity and x- and y-momentum equations for the flow and mass conservation equation for sediment. The two-dimensional modeling of the layer-averaged equations with a finite element method has two important aspects; the dissipative algorithm and the front tracking technique. Since the standard Galerkin method yields spurious oscillations when applied to convection-dominated flows, the dissipative-Galerkin technique having a selective dissipation property is used. Also, in order to track the moving front accurately, a deforming grid generation technique based on the arbitrary Lagrangian-Eulerian approach is employed for the two-dimensional problem. The developed numerical procedure is applied to a decelerating-depositional turbidity current generated in the laboratory experiment by Luthi (1981). Time-dependent profiles for the current thickness and layer-averaged velocity field and volumetric concentration are obtained. The relevant depositional structure by this underflow event is estimated by incorporating the double grid finite element method into the flow algorithm.