A moving particle semi‐implicit method for free surface flow: Improvement in inter‐particle force stabilization and consistency restoring

Abstract

The moving particle semi‐implicit (MPS) method has been widely applied in free surface flows. However, the implementation of MPS remains limited because of compressive instability occurred when the particles are under compressive stress states. This study proposed an inter‐particle force stabilization and consistency restoring MPS (IFS‐CR‐MPS) method to overcome this numerical instability. For inter‐particle force stabilization, a hyperbolic‐shaped quintic kernel function is developed with a non‐negative and smooth second order derivative to satisfy the stability criterion under compressive stress state. Then, a contrastive study is conducted on the contradiction between the common understanding of the conventional MPS hyperbolic‐shaped kernel function and its performance. The result shows that the conventional MPS hyperbolic‐shaped kernel function can easily cause violent repulsive inter‐particle force and then lead to the compressive instability. Therefore, the first order derivative of the modified hyperbolic‐shaped quintic kernel function is recommended as the form of the contribution of the neighbor particles to achieve a more stable inter‐particle repulsive force. For consistency restoring, the Taylor series expansion and the hyperbolic‐shaped quintic kernel are combined to improve the accuracy of the viscosity and pressure calculation. The IFS‐CR‐MPS algorithm is subsequently verified by the inviscid hydrostatic pressure, jet impacting, and viscous droplet impacting problems. These results can be used for choosing kernel function and the contribution of neighbor particles in particle methods. Copyright © 2016 John Wiley & Sons, Ltd.

Bow Flare Water Entry Impact Prediction and Simulation Based on Moving Particle Semi‐Implicit Turbulence Method

“…K. S. Kim and M.-H. Kim [24] extended MPS method to a multiphase system with multiple interfaces to solve the multifluid multi-interface problems; the results are compared with corresponding experiment results with three liquids. Xiang and Chen [25] proposed an interparticle force stabilization and consistency restoring MPS method to overcome the compressive instability that occurred under compressive stress states. A new and simple free surface detection criterion is proposed by Wang et al [26] to enhance the free surface recognition in the MPS method.…”

“…In MPS method the boundary pressure particles are involved in the solution of Poisson equation, satisfying (25); in the simulation process these particles are defined as free surface particles incorrectly. So in the determination procedure a mixed method is applied; in the simulation the fluid is possible to be broken and the jet flow phenomenon happens; in these situations the particle number density is less than the others, so these particles can be defined as free surface particles directly; the determination equation can be expressed as…”

Mesh-Free MLS-Based Error-Recovery Technique for Finite Element Incompressible Elastic Computations

“…Chen et al [3] summarized the surveys of mesh-free method developed to address the weaknesses of the finite element approach. Some the recent developments in alternative finite element methods (FEM) are the generalized finite element method [4], the extended finite element technique [5], the smoothed finite element method [6], the smoothed-particle-hydrodynamics method [7], the reproducing kernel particle method [8], and the moving-particle semi-implicit method [9]. A number of materials used in industry have very high bulk moduli in comparison with the shear modulus, i.e., nearly incompressible materials, and materials with large deformations may also be treated as incompressible.…”