Performance Comparison between Semi-Lagrangian and Eulerian Numerical Solutions for Two-Dimensional Surface Flows in Basin Irrigation

Abstract

To achieve efficient simulation for surface shallow-water flows in large-scale basin irrigation, a semi-Lagrangian numerical solution for two-dimensional shallow-water equations in unstructured spatial cells was developed. In this numerical solution, all state variables were defined at the finite-volume cells and presented piecewise constant distribution. A redistribution method of the state variable values for the inner node of a spatial cell was developed and can strictly preserve mass conservation. Then, a simple displacement formula along a characteristic-line was applied to connect the variable values between a unknown and its adjacently known time steps of the semi-Lagrangian form of two-dimensional shallow-water equations. The water level gradient term was specially treated to accurately balance the water level distribution at the wet or wet–dry spatial cell interface. Simultaneously, an existing finite-volume method with a fully implicit temporal solution for the Eulerian form of two-dimensional shallow-water equations in a triangular spatial cell was selected as a comparative model. Finally, a performance comparison between the semi-Lagrangian and Eulerian numerical solutions was analyzed based on three basin irrigation experiments. The results show that the semi-Lagrangian and Eulerian numerical solutions presented similar average relative errors between the observed and simulated data. The semi-Lagrangian numerical solution exhibited lower mass conservation ability, but its water quantity balance errors were less than 0.3% for three experiments. The semi-Lagrangian numerical solution was six times more computationally efficient than the Eulerian numerical solution in central processing unit (CPU) time. Thus, the semi-Lagrangian numerical solution is more suitable to simulate shallow-water flows in basin irrigation.