Comparison of two projection methods in SPH for modeling flow under a gate

Modeling free surface flow is a challenging problem in hydraulic research. The objective of this research is to compare those methods for simulation of flow around hydraulic structures. Accordingly, Incompressible SPH (ISPH) methods, with two different projection methods to enforce incompressibility, are utilized to model flow under a gate and then compared to each other from mathematical and numerical viewpoints. Moreover, the effect of pressure term approximation on conservation equation of mass and momentum with two different relations is investigated by error index. For verification of ISPH results, VOF method is applied to similar gate problem. Results show that two methods of enforcing incompressibility are numerically and mathematically equivalent if proper approximation terms are used in SPH method. Furthermore, VOF and ISPH results are in excellent agreement. Besides, two pressure terms obey similar chaotic error trend for inner and all particles (inner plus free surface).