Solving 2-D Slamming Problems by an Improved Higher-Order Moving Particle Semi-Implicit Method

A higher-order moving particle semi-implicit (MPS) method was further developed to solve 2-D water entry problems. To overcome the inconsistency in the original MPS methods, a pressure gradient correction was implemented to guarantee the first-order consistency of the gradient. The corrective matrix was modified by using the derivative of the kernel function. A particle shifting technique was also applied to improve the numerical stability. Validation studies were carried out for water entry of a rigid wedge with the tilting angles of 0 degrees, 10 degrees, and 20 degrees, and two rigid ship sections. Convergence studies were conducted on domain size, particle spacing, and time step. A particle convergence index method was proposed to evaluate numerical uncertainties in the improved MPS method. Uncertainties in numerical solutions due to spatial discretization were calculated. The predicted impact pressures and forces by the present method are in good agreement with experimental data.