The Smoothed Particle Hydrodynamics Method And Its Application In Shallow Water

Smoothed Particle Hydrodynamics (SPH), as a meshfree method, has been widely applied to computational Fluid Dynamics. Compared with the traditional finite difference method (FDM), or finite element method (FEM) or finite volume method (FVM), SPH method has its unique advantages. The advance in theoretical research and application fields of SPH method has been reviewed from the angle of methodology. Some innovations about algorithm improvement and algorithm application are made, some significant improvement measures are proposed and the application fields are broadened. Our major researches are as follows:1. For improving the stability and computational accuracy of SPH, on the basis of theoretical analysis of basic algorithm and improved algorithm, it is pointed out that there are some problems about stability, accuracy and efficiency of algorithm. Through the theoretical analysis of numerical precision of algorithm and verification of numerical simulation, the strategy is introduced to improve algorithm stability and computational accuracy.2. The research is conducted on the application of SPH in the shallow water equations, including particle splitting algorithm and discontinuous solutions algorithm.(1) A basic method is proposed for solution of one-dimensional and two-dimensional shallow water equations in SPH, the discussion and analysis are conducted of some techniques for solution of shallow water equations, including processing of stability term, initializing arrangement of particles and selection of smooth lengths, and some implementation techniques are summed up of SPH methods suitable for solution of the shallow water equations.(2) An algorithm of particle splitting is discussed for the solution of shallow water equations. For improving the stability of algorithm and the accuracy of local flow fields, the particle splitting is exploited in the area with numerical abrupt change area in the flow field or the area with fewer particles and the uniformity of particle distribution is improved by increasing some particles in order to satisfy the demand of kernel function approximation and particle approximation for particle distribution in the flow field. The splitting algorithm broadens the application of SPH in interface of Water area and the area without water.(3) The method for solution of shallow water equations is discussed in view of Riemann problem. For capturing the shock wave phenomenon in dam break and keeping the stability of algorithm, the discontinuous solution is introduced into SPH method, and the interaction between the paired particles is seen as discontinuity. Riemann problem will be combined with SPH method, which can improve the capacity of capturing shock waves.3. Based on triangular mesh generation technology in grid method, a feasible method of two-dimensional data preprocessing and post-processing of SPH is introduced. Data preprocessing techniques can be implemented with complex boundary initial particle flow field configuration, data post-processing technology is helpful for using the existing fluid dynamics analysis software for numerical analysis and graphical display needs.