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

移动粒子半隐式（MPS）方法是一种求解复杂流动问题的无网格流体力学数值计算方法。 无网格方法使用一组任意分布的粒子，而不是一个固定的网格布局，以解决不同的边界和界面的控制方程。 在该方法中，控制方程被离散为一组在拉格朗日坐标系中运动的任意分布的粒子。 有限数量的移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方法于1996年引入，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）的替代方案来求解Navier-Stokes方程。 该方法具有适应性强、能模拟水面变化和流体界面等特点，在水流模拟中具有一定的优势。 以前的研究也表明，粒子方法预测简单的稳定流的速度分布良好的能力。然而，对于溃坝、水跃、掺气、散粒体流动等瞬变流的速度和压力分布研究较少。 在以往的研究中，水面实验数据主要用于模型的校正。对超临界流动、射流、传热和流固耦合等工程问题进行了数值模拟，预测了自由表面的位置。瞬态流体流动的速度、压力等细节信息往往被忽略。多年来，人们一直在研究MPS方法，以提高稳定性和计算速度。深入研究MPS的理论和基本原理，将有助于MPS方法的进一步完善，使其成为一种更通用的工程仿真技术。 本研究的主要内容有三：（1）提高MPS模型的精度和稳定性;（2）模型的应用;（3）多相MPS模型的开发。在第一阶段，将修改MPS方法，以提高精度，稳定性和粒子动态细化。 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。第一个应用案例是利用MPS模式研究滑坡诱发波及其流场。 宽顶堰的流量系数、流速分布、临界水深位置及水流分离区的数值研究将是另一个应用。 第三个工程应用是应用MPS来模拟颗粒流。实验室数据将用于所有应用程序，以验证模型。 第三部分是在MPS模型中加入质量输运方程，建立两相流模型。随后将模拟泥沙输移和气泡夹带。

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.