Dynamic-wave cellular automata framework for shallow water flow modeling

Abstract

A new dynamic-wave cellular automata framework for two-dimensional (2D) shallow water flow (SWF) modeling is herein proposed. During the last decade, the concept of cellular automata (CA) has been widely adopted to develop various 2D shallow water flow models. Such CA models use simple transition rules that only consider the conservation of mass and neglect the conservation of momentum, as a result, the models behave like the non-inertia wave approximation which are not suitable for modeling strong discontinuous flows (i.e., transcritical flows and wet-dry interfaces). To overcome this limitation, the present study proposes a new CA framework (SWFCA) for 2D shallow water flow modeling, in which the Bernoulli hydraulic head is adopted to replace water level as the key factor to determine water movements. A novel methodology for linking water depths and velocities in the framework is developed. Model verification is carried out through four cases of regular flows and six benchmark cases with strong discontinuous flows. Model efficiency assessment is also conducted to analyze the numerical performance under various flow conditions. The outcomes indicate that the proposed SWFCA model and a non-inertia wave CA-based model (WCA2D) both provide satisfactory results on regular flows. In modeling strong discontinuous flows, the SWFCA model performs better than the WCA2D model and provides the same accuracy as the finite volume model with a HLLC scheme (FV-HLLC). In the aspect of moving wet-dry interfaces and flows under the partially wet condition, the SWFCA model can achieve higher accuracy than the FV-HLLC model. The numerical efficiency of the SWFCA model relates to the flow conditions involved. As the portion of strong discontinuous flows in the computational domain is increasing, the SWFCA model can be up to 305.5% and 121.0%-1282.2% faster than the WCA2D model and the FV-HLLC model, respectively. This novel CA-based framework has been proved its accuracy and efficiency for shallow water flow modeling. Therefore, it has considerable potentials as a useful tool for real-time flood inundation modeling.