New Complex Methods for Calculating Water Level Gradient in Computational Hydrodynamic Models

Water level gradient is an important driver of water flow; therefore, its calculation method strongly affects the performance of a computational hydrodynamic model. Three new complex methods for calculating the water level gradient were proposed in this work. These new methods along with four existing methods, including two basic methods, the downwind and central difference methods, and two complex methods proposed by previous researchers, were tested by being adopted in a one-dimensional numerical model to simulate three circumstances of water flow. These circumstances included a dam-break water flow on a dry riverbed, a dam-break water flow on a wet riverbed, and a water jump flow. Numerical predictions of flow characteristics including discharge, velocity, and water depth, were meticulously compared with theoretical solutions. Results showed that for the case of dam-break water flow on a dry riverbed, the three new methods did not demonstrate a notable advantage over the existing methods; while for the cases of the dam-break water flow on a wet riverbed and the water jump flow, the three new methods showed advantages in terms of stability or accuracy. The methods proposed in this paper can be applied to both one and two-dimensional computational hydrodynamic models to improve their performance.