A Comparison between Shallow Water and Level Set Methods in Simulating Water Flooding

S. Cagliari1, A. Barbagallo1, R. Sinatra1, G. Petrone1
1BE CAE & Test S.r.l., Viale Africa 170 - Sc. A, 95129, Catania, ITALY
Published in 2023

In this paper, the COMSOL Certified Consultant BE CAE & Test presents a comparison between two approaches exploitable in COMSOL Multiphysics® to simulate water flooding. Flooding is an argument of high interest both in industrial engineering and in environmental science. Dam breaks, rivers overflowing as well as tsunami effects are just a few exemplar applications that can be mentioned. From a simulation point of view, the key aspect in simulating this kind of physical event consists in choosing a suitable method to manage a free-surface flow. In the software environment, this item can be approached by different physic interfaces, such as the Shallow Water and the Level Set, both available in the CFD Module. The Shallow Water (SW) equations are derived from the Navier-Stokes equations, simplified under the main assumption that the horizontal length / velocity scale is much greater than the vertical length / velocity scale. Under this condition, the vertical velocity component is not directly solved in the momentum equations: its value is recovered from the continuity equation once the momentum equations are solved. Otherwise, the Level Set (LV) method belongs to more complex methods devoted to track a moving interface between immiscible fluid phases by solving further PDEs together with the Navier-Stokes equations. In the Level Set method, one scalar variable only is defined in the [0; 1] range to identify each phase in fluid-dynamic solution, being 0.5 the level set value identifying the interface location.
The aim of this work is to use SW and LV in a real-world application and to compare these approaches each other, highlighting strong and weak points for each one. The proposed application concerns a system for water recovery, in which a high-level basin is connected to a ground-level basin by different ducts. Transient simulation of water flowing when the span of the doorway is open - and consequent ground level basin flooding - is implemented and solved exploiting both previously discussed approaches. A relative comparison is then made, paying attention to several usual aspects to consider in numerical modelling, such as theoretical limits, flexibility in application, implementation complexity, required hardware resources and computational time, robustness of the model and achievable convergence, reliability and quality of results, post-processing opportunities.