Front-fixing modeling of turbidity currents

A mathematical model is developed for an unsteady, one-dimensional, single-layer, depth-averaged turbidity current driven by sediment of uniform size and temperature difference in a stratified ambient fluid. As both inflow and outflow current boundaries move in time, they are fixed by a suitable transformation of coordinate system. A deforming grid method overcomes the problem of a numerically 'dry' bed associated with the standard fixed-grid approach. The explicit Ultimate Quickest method of the third order in both time and space has been selected as particularly appropriate for solving hyperbolic governing equations that admit shocks and discontinuities. The original method is significantly improved in terms of computational efficiency by the introduction of time stretching that follows grid stretching in the longitudinal direction, thus maintaining the initial Courant number. The model is also capable of tracking the evolution of the bed in response to erosion and deposition of sediment.