Improvement of Mesh-free Particle Method for Free Surface Flow Simulation

运动粒子半隐式（MPS）方法是一种基于无网格的求解复杂流动问题的数值计算流体力学技术。无网格方法使用一组任意分布的粒子，而不是固定的网格布局来求解不同边界和界面的控制方程。该方法将控制方程离散到一组在拉格朗日坐标系中运动的任意分布的粒子上。有限数量的运动粒子被应用于填充系统域。每个粒子都有一组场变量，如质量、浓度和动量。MPS方法是1996年引入的，作为基于网格的方法如有限差分法、有限元法和有限体积法的替代方法来求解Navier-Stokes方程。该方法具有较强的适应性和模拟水面变化和流体界面的能力，在流动模拟中具有优势。

The Moving Particle Semi-implicit (MPS) method is a mesh - free based numerical computation fluid dynamics technique for solving complex flow problem. The mesh-free methods use a set of arbitrarily distributed particles as opposed to a fixed mesh grid layout to solve governing equations for diverse boundaries and interfaces. In this method, governing equations are discretized over a set of arbitrarily distributed particles moving in the Lagrangian coordinate system. A finite number of moving particles are applied to fill the system domain. Each particle possesses a set of field variables such as mass, concentration and momentum. MPS method was introduced in 1996 as an alternative to mesh-based methods such as Finite Difference Method, Finite Element Method and Finite Volume method to solve the Navier-Stokes equations. This method is advantageous in flow simulation due to its adaptability and capability of simulating water surface variation and fluid interfaces. Previous studies also showed the capacity of the particle method for predicting good velocity profiles for simple steady flows. However, the velocity and pressure distribution for transient flow such as dam break, hydraulic jump, air entrainment, and flow of granular material are seldom. In most of previous researches, experimental data of water surface are mainly for model calibration. The engineering problems like super critical flows, jet flow, heat transfer and fluid structure interaction are simulated for the prediction of the location of free surface. The detailed information of transient fluid flow such as velocity and pressure are always neglected. Over the years, MPS method has been studied to improve the stability and computing speed. Further study to understand the theory and the basic of MPS will improve the MPS method to make it a more general engineering simulation technique. There are three main subjects in this proposal: (1) improvement to the accuracy and stability in MPS model, (2) model application and (3) development of a multiphase MPS model. In the first phase, the MPS method will be modified to improve the accuracy, stability and particle dynamic refinement. The collision model and repulsive force in gradient models and the integration of the Laplacian model will be studied and modified. The first application case is using the MPS model to investigate the landslide induced waves and its flow field. Numerical study of broad-crested weirs including discharge coefficients, velocity distributions, location of critical depth, and flow separation zone will be another application. The third engineering application is applying MPS to model granular flows. Lab data will be used in all applications to verify the model. The third part of the project is to develop a two phase flow model by adding the mass transport equation to MPS model. The sediment transport and air bubble entrainment will be simulated afterwards.