Improved MPS method with variable-size particles

Using variable-size particles in the moving particle semi-implicit method (MPS) could lead to inaccurate predictions and/or numerical instability. In this paper, a variable-size particle moving particle semi-implicit method (VSP-MPS) scheme is proposed for the MPS method to achieve more reliable simulations with variable-size particles. To improve stability and accuracy, a new gradient model is developed based on a previously developed MPS scheme that requires no surface detection MPS. The dynamic particle coalescing and splitting algorithm is revised to achieve dynamic multi-resolution. A cubic spline function with additional function is employed as the kernel function. The effectiveness of the VSP-MPS method is demonstrated by three verification examples, that is, a hydrostatic pressure problem, a complicated free surface flow problem with large deformation, and a dynamic impact problem. The new VSP-MPS scheme with variable-size particles is found to have balanced efficiency and accuracy that is suitable for simulating large systems with complex flow patterns. Copyright (C) 2015 John Wiley & Sons, Ltd.