New modified gradient models for MPS method applied to free-surface flow simulations

In this paper, two modified pressure gradient models based on Taylor series expansion are proposed to enhance the higher order source term MPS (MPS-HS) method. The modified models consist of gradient correction matrices applied to the existing (base) pressure gradient models. To validate the modified pressure gradient models first hydrostatic pressure test is simulated and compared to both the base and modified MPS methods. Using the modified models are shown to reduce unphysical pressure oscillations observed in the base models. Second, an evolution of an elliptical drop in a 2D flow field is examined and shown to verify the models. Third, the proposed models illustrated appropriate stability and consistency properties against analytical solutions when an altered gravitational acceleration was superimposed to the hydrostatic pressure test. In addition, an improved performance is observed when Higher order Laplacian (HL) and Error-Compensating Source (ECS) of the Poisson Pressure Equation (PPE) schemes are coupled with the modified pressure gradient models compared to coupling them with the base gradient models. Finally, the modified MPS methods enhanced performances are validated in a free-surface flow simulation for a dam break problem with impact pressure, and a violent sloshing flow in a rectangular tank when compared to the base MPS methods against an existing experimental data.