Research On Theory And Applications Of A Numerical Flow Model Based On MPS Method

The MPS method, adopting N-S equations as governing equations, is a new numerical approaches in the hydrodynamic calculation, which is a complete particle method based on Lagrangian concept. It is of especial advantages comparing with the Eulerian grid numerical approach and is more convenient to be used in solving the flow problems with violent deformation of free surface, and in dealing with the rigid boundary of complex shape. Consequently, research on the method is not only of great significance in theory but is believed to have good prospect of application.An improved theoretical model is proposed based on a formerly-presented MPS method. According to large number of numerical experiments, discussions are carried out on the effect of different form of kernel function to the numerical results and the stability and the spline function used in the SPH model is finally introduced as the kernel function. Some modifications are also carried out for the diffusion and gradient sub-models to properly reflect the interactions among particles.The improved flow model based on the MPS method is applied to the simulation of the collapsing processes of a vertical 2-D water column to see how the viscosity and friction term affect the numerical results of pressure. It is found that the viscosity affects the sharpness of the pressure peak and the friction term affects the phase of the pressure process. An apparatus is designed to measure the impinging pressure on a vertical board reduced from water column collapsing. Good agreement between modeled and measured results of pressure process can be achieved by adjusting the values of the viscosity and the friction coefficient.A numerical wave flume is established based on the MPS method, which is used to simulate the propagation process and run-up and run-down of a soliton. The spatial profiles of velocity in the propagation process of a soliton are computed. More over, the propagation and reflection progress of linear wave is simulated. It is indicated that the modeled wave profiles are in good agreement with analytical solutions and the obtained maximum value of the run-up of solitary waves with various relative incident wave height agree well with the experimental data.