A physics-compatible solver for turbidity currents

Abstract

Turbidity currents are an essential agent of sediment transport from shallow to deeper waters. Detailed measurements of the velocity field or particle concentration are only available by means of accurate numerical simulations. In this thesis, a DNS solver for turbidity currents is presented based on the MEEVC scheme, a mass, energy, enstrophy and vorticity conserving solver for the 2D incompressible Navier-Stokes equations with periodic boundary conditions. The construction of the solver consists of two separate steps: the prescription of slip boundary conditions and the implementation of a transport equation for the particle phase. Tangential velocity boundary conditions cannot be imposed strongly because the velocity is sought in the function space H(div). To this end, three methods are proposed for the weak enforcement of the tangential velocity component by means of vorticity boundary conditions. Of these methods, kinematic Neumann boundary conditions prove to be the most effective and are used for the construction of a turbidity current solver. An equilibrium Eulerian approach for the particle phase is implemented and the resulting solver is proved to satisfy the discrete energy balance equations up to a residual. This residual does not accumulate over time and no artificial dissipation of energy is introduced into the system. The 2D lock exchange test case is computed and comparisons are made with reference results. The numerical results indicate that the solver is capable of capturing the essential dynamics of the flow in coarse grids.