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数值计算流体力学技术，用于求解复杂流动问题。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。在这种方法中，控制方程被离散在一组在拉格朗日坐标系中运动的任意分布的质点上。应用有限数量的移动粒子来填充系统域。每个粒子都有一组场变量，如质量、浓度和动量。MPS方法是1996年提出的求解N-S方程的有限差分法、有限单元法和有限体积法等网格方法的替代方法。该方法具有较强的适应性和模拟水面变化及流体界面的能力，因此在水流模拟中具有一定的优势。然而，关于溃坝、水跃、夹气、颗粒物质流动等瞬变流的速度和压力分布却很少。在以往的研究中，水面的实验数据主要用于模型校正。对超临界流动、射流、换热、流固耦合等工程问题进行了数值模拟，预测了自由面位置。多年来，为了提高计算的稳定性和计算速度，人们对MPS方法进行了深入的研究。通过对MPS理论和基础的深入研究，将改进MPS方法，使其成为一种更具通用性的工程模拟技术。*该方案主要包括三个方面的内容：(1)提高MPS模型的精度和稳定性；(2)模型应用；(3)多相MPS模型的发展。在第一阶段，将对MPS方法进行改进，以提高精度、稳定性和粒子的动态精化。对梯度模型中的碰撞模型和排斥力以及拉普拉斯模型的积分进行了研究和修正。第一个应用实例是利用MPS模型研究滑坡诱发的波浪及其流场。宽顶堰的数值研究将是另一个应用，包括流量系数、流速分布、临界深度位置和分流区。第三个工程应用是应用MPS来模拟颗粒流。将在所有应用程序中使用实验室数据来验证模型。项目的第三部分是将传质方程加入到MPS模型中，建立了两相流模型。随后将对泥沙运动和气泡卷吸进行模拟。

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.