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

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.