Evaluation Of A Hybrid Eulerian-LagrangianMethod For Free Surface Flows With MaterialTransport

Abstract

A combined Eulerian-Lagrangian method (ELM), with applications to the two-dimensional shallow water wave equations and to the convectiondispersion equation has been evaluated. A semi-implicit formulation of the method is derived and discussed. The gradient of water surface elevation in the momentum equations and the velocity divergence in the continuity equation is discretized implicitly. An explicit Eulerian-Lagrangian approach with large time steps is used to discretize the convective terms. A complete elimination of the stability restriction may be achieved, so that the time step becomes independent of wave celerity. The same technique has been applied to the depth averaged convection-diffusion (transport) equation. The validation of the model was performed by comparison with experimental results, as well as with analytical (where available) solutions and results obtained with other schemes. Results obtained from two-dimensional simulations of flow fields with irregular boundaries and variable bathymetry are presented to indicate the possible industrial application of the model. The method introduced here occasionally displays artificial diffusion as well as spurious oscillations, but may be controlled either by reducing the spatial increment, or by changing the time step of the grid used to solve the convection problem. Transactions on Ecology and the Environment vol 5, © 1994 WIT Press, www.witpress.com, ISSN 1743-3541