Random Walk Particle Tracking for Convection-diffusion Dominated Problems in Shallow Water Flows

Abstract

This paper deals with a Lagrangian stochastic approach to solve the advection-diffusion equation of a scalar tracer inflow based on random walk particle tracking (RWPT) of a fine number of particles that describe the tracer. The water flow is governed by the shallow water equations that are solved using a finite volume upwinding scheme on a non-structured triangular mesh. Results are presented for two problems, pure advection in a square cavity and pollutant advection in the strait of Gibraltar, that demonstrate the performance, accuracy, and the flexibility of the RWPT method to examine the process of pollutant convection by comparing predictions with those from the Eulerian approach. The Lagrangian approach is shown to have advantages in terms of the high level of simplicity and stability relative to the Eulerian approach.