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

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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.