Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> A. CLASSICAL SOLID WALL BOUNDARY PROCESSING <s> An implementation of the smoothed particle hydrodynamics (SPH) method is presented to treat two-dimensional interfacial flows, that is, flow fields with different fluids separated by sharp interfaces. Test cases are presented to show that the present formulation remains stable for low density ratios. In particular, results are compared with those obtained by other solution techniques, showing a good agreement. The classical dam-break problem is studied by the present two-phase approach and the effects of density-ratio variations are discussed. The role of air entrapment on loads is discussed. <s> BIB001 </s> Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> A. CLASSICAL SOLID WALL BOUNDARY PROCESSING <s> The impact of a single wave generated by a dam break with a tall structure is modeled with a three-dimensional version of the smoothed particle hydrodynamics method. The method is used to analyze the propagation of a long wave and the force it exerts on a tall structure located in a region with vertical boundaries. Velocities and forces obtained from a numerical model are shown to be in good agreement with laboratory measurements. The effect of having a dry bed in front of the dam prior to the dam break versus a wet bed in the experiment is discussed. <s> BIB002 </s> Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> A. CLASSICAL SOLID WALL BOUNDARY PROCESSING <s> Smoothed particle hydrodynamics (SPH) is a meshfree particle method based on Lagrangian formulation, and has been widely applied to different areas in engineering and science. This paper presents an overview on the SPH method and its recent developments, including (1) the need for meshfree particle methods, and advantages of SPH, (2) approximation schemes of the conventional SPH method and numerical techniques for deriving SPH formulations for partial differential equations such as the Navier-Stokes (N-S) equations, (3) the role of the smoothing kernel functions and a general approach to construct smoothing kernel functions, (4) kernel and particle consistency for the SPH method, and approaches for restoring particle consistency, (5) several important numerical aspects, and (6) some recent applications of SPH. The paper ends with some concluding remarks. <s> BIB003
The boundary force method works by setting a series of the relative positions of particles around the fixed solid wall boundary, and force is exerted on the flow of particles by boundary particles. This force is repulsive and decreases as the distance increases. The boundary force method can handle complex boundary conditions, but the choice of force is usually only based on experience and is difficult to specify. An excessively small force cannot push the particles through the border, but if the force is too large, then moving particles could penetrate through the border  . The mirror particle method works by mapping boundary particles to the solid wall to represent the solid region BIB001 . The boundary particles have the same mass and density as the corresponding flow particles, with an opposing velocity in the same direction. Figure 5 shows the principal details of themirror particle method. The mirror particle method has a good property of conservation and accuracy, but it is difficult to generalize to a complex and less accurate calculation area. The coupling boundary method works by converting the solid walls into a series of boundary points, where these boundary points are some properties (mass, density, and pressure) of the fluid mass. In the solution process, the presence of boundary points is akin to the situation to solve a continuous equation or a state equation, such that the boundary problem is coupled with the process of solving an equation, and the explicit boundary condition solution is avoided BIB002 , BIB003 .