Residual-based variational multi-scale modeling for particle-laden gravity currents over flat and triangular wavy terrains

In this paper, a numerical formulation for simulating dilute particle-laden gravity currents at large Reynolds number (Re) is developed using a residual-based variational multi-scale formulation (RBVMS), in which the coupling between the velocity fine scales and density concentration equation residual is represented. The proposed formulation is utilized to simulate the lock-exchange particle-laden gravity currents at Re=10,000. Firstly, we validated the proposed formulation by simulating the gravity currents over flat terrain. Flow statistics are thoroughly compared against high-resolution simulation results such as DNS or experimental results in the literature. It shows the RBVMS formulation presented here can reproduce quite accurate results with much lower mesh resolution. Then, the particle-laden gravity currents over triangular wavy terrains with changing wave heights are simulated. The effect of the wave height on the flow statistics is investigated.