An accurate and stable multiphase moving particle semi‐implicit method based on a corrective matrix for all particle interaction models

Abstract

Summary The Lagrangian moving particle semi‐implicit (MPS) method has potential to simulate free‐surface and multiphase flows. However, the chaotic distribution of particles can decrease accuracy and reliability in the conventional MPS method. In this study, a new Laplacian model is proposed by removing the errors associated with first‐order partial derivatives based on a corrected matrix. Therefore, a corrective matrix is applied to all the MPS discretization models to enhance computational accuracy. Then, the developed corrected models are coupled into our previous multiphase MPS methods. Separate stabilizing strategies are developed for internal and free‐surface particles. Specifically, particle shifting is applied to internal particles. Meanwhile, a conservative pressure gradient model and a modified optimized particle shifting scheme are applied to free‐surface particles to produce the required adjustments in surface normal and tangent directions, respectively. The simulations of a multifluid pressure oscillation flow and a bubble rising flow demonstrate the accuracy improvements of the corrective matrix. The elliptical drop deformation demonstrates the stability/accuracy improvement of the present stabilizing strategies at free surface. Finally, a turbulent multiphase flow with complicated interface fragmentation and coalescence is simulated to demonstrate the capability of the developed method.

Imposing accurate wall boundary conditions in corrective‐matrix‐based moving particle semi‐implicit method for free surface flow

“…Namely, one layer of wall particles to represent the real boundary and two/three layers of dummy particles to compensate the neighbor support of fluid particles. In the previous work, 31,32 both dummy and wall particles are considered in calculating corrective matrix. Therefore, it is necessary to specify the variable values for these wall and dummy particles based on boundary conditions.…”

“…After the new schemes are applied to internal particles, the boundary condition of pressure is imposed differently from the existing methods. 31,32 The overall algorithm is slightly adjusted based on the authors' recent one that is designed for highly viscous flow. 47 The overall algorithm and enforced boundary conditions are as follows.…”

“…Particularly, the particle shifting (PS) method 25 can stabilize simulations even if the coherent particle distributions would take place. After PS is applied, the high order formulations restoring discretization consistency (eg, moving least squares method, 26 least square moving particle semi-implicit (LSMPS) method, 27 kernel gradient correction in SPH, 28,29 and corrective matrix schemes in MPS [30][31][32] ) can produce accurate and stable discretization for the inside particles that are not near boundaries. In this study, the corrective matrix schemes are adopted due to their simplicity.…”

Machine‐learning‐based surface tension model for multiphase flow simulation using particle method

“…In contrast to Eulerian methods, interfaces are represented by moving particles self‐adaptively without special treatment. Popular Lagrangian methods include smoothed particle hydrodynamics (SPH), 5,6 moving particle semi‐implicit (MPS) 7,8 and finite volume particle (FVP) 9,10 methods. In this article, we employ the particle method in the Lagrangian framework to study multiphase flow with surface tension.…”

“…This work is based on MPS method. During the past two decades, significant improvements have been achieved to improve the accuracy and stability of the MPS method, including corrective gradient model, 21,22 high‐order Laplacian model, 8,23,24 least‐square MPS, 25 and conservative pairwise‐relaxing method 26 . Extensive study is conducted in multiphase flow simulation using MPS 27‐32 .…”