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Contents Chapter 1 Introduction…………………………………………………………………1 1. 1 Computational fluid dynamics 1.1.1 Grid methods…………………………………………………………………1 1.1.2Mesh- free methods……… 1.2 Polygon wall boundary condition………………… Chapter2 MPS method…………………………………………4 2.1 Governing equations 2.2 Weight function and discretization models………………4 2.3 Derivation of mPs 2.4 Wall boundary conditions………………………………………………………7 Chapter 3 Boundary conditions in MPS 3.1 Five types of wall boundary conditions…………………………………9 3. 1. 1 Dummy particles 3. 1.2 Mirror particles 3.1.3 Boundary forces……………………………………………………17 3.1.4 Unified semi-analytical wall boundary condition 3.1.5 Polygon wall boundary condition……………………………20 3.2 Initialization of polygon wall boundary condition 3.3 Discretization models of polygon wall boundary condition…………23 3.3.1 Derivation process 3.3.2 Discretization equations……………………………………………24 Chapter 4 Improved wall calculation of polygon wall boundary condition 4.1 Problems of polygon wall boundary condition…………………………28 4.2 Improvement of wall calculations 4.2.1¢ó lustration of improved method…………………………………32 4.2.2 Calculation of the wall weight function…………………………32 4.3 Numerical examples 4.3.1 Accuracy of wall weight function at different positions…………34 4.3.2 Classic dam break simulation 4.3.3 Dam break simulation with a wedge in the water tank……………42 4. 4 Summary Chapter 5 Boundary particle arrangement technique in polygon wall boundary condition 5. 1 Boundary particle arrangement technique 5.1.1 Construction of the boundary particles……………… 5. 1.2 Construction of dummy particles 5.2 Adjustment of collision coefficients………………52 5.3 Simulation results 5.3.1 Dam break with a wedge 5.3.2 Simulation of complex geometry 5. 4 Summary Chapter 6 Improvement of pressure distribution in polygon wall boundary condition 6. 1 Research progress 6.2 Improved particle-polygonal meshes interaction models 6.2.1 Re-derivation of polygon wall boundary condition . ........72 6. 2.2 Problem of present source term in the polygon wall boundary condition 6.2.3 Improvement of source term in the polygon wall boundary condition 6.2.4 Improvement of gradient model ...... 6.2.5 Surface detection 6.3 Results and discussions………………………… 6.3. 1 Hydrostatic pressure 6.3.2 Dam break simulation……………… 6.3.3 Complex geometry simulations 6.4 Summary… References Noun index