Finite-Volume and Shock-Capturing Shallow Water Equation Model to Simulate Boussinesq-Type Lock-Exchange Flows

Abstract

Among the various applications of the shallow water equations (SWEs) is the simulation of gravity currents (GCs). The SWEs are used as an alternative to track GC motion without explicitly dealing with turbulent processes, and constitute an intermediate solution between simpler integral models and more comprehensive models based on the Navier-Stokes equations. While the SWE equations have been successfully applied to a number of problems involving the release of dense fluids into deep ambient conditions, a more complex application is the simulation of the lock-exchange problem. In this particular problem, the ambient velocity influences the velocity as well as the shape of the GC, especially in the initial slumping stage. Features resembling discontinuities between the two layers are generated, and one numerical solution strategy has been to explicitly track such discontinuities. This work presents a shock-capturing, two-layer SWE model to simulate lock-exchange flows and its discontinuities. The main contributions are a reformulated mathematical model that incorporates the upper layer effects to the GC flow as well as a more efficient numerical solution for the flow at the GC front. The resulting numerical model was implemented using the finite-volume method (FVM) with an approximate Riemann solver, and the results compare well to existing numerical models as well as experimental data collected during this investigation.