An Investigation Of Improved SPH And Its Application For Free Surface Flow

Smoothed Particle hydrodynamics (SPH) was invented in 1977, which was considered as the first meshfree method. The investigation of theory and application got fast development in the last 30 years. More and more scholars focused their interesting on this topic. The computing domain of SPH is divided by a mass of particles, which is different of traditional numerical methods.It escapes the limitation of mesh making. Many research fields, for example, strongly non-linear wave impact, high velocity motion, fracture of brittle solid, underwater explosion, can be simulated by SPH effectively, which are difficult for traditional mesh methods.SPH also obtains other advantages, e.g., the free surface is easy to handling, the program is not difficult to write, last results can be shown directly and so on.Based on the further research of present SPH foundation, an improved kernel approximation is introduced, named second order kernel approximation SPH (K2_SPH), according to the shortcoming of traditional SPH. After a series of error analysis and different types of wave flow simulation, advantages and disadvantages of two SPH methods are obtained, which are important for further investigation. The content of this thesis includes following parts:Firstly, basic theory and corresponding numerical techniques of SPH are introduced, which including kernel approximation and particle approximation, boundary handling method, artificial pressure approximate method and artificial viscosity, et al. According to low accuracy feature of traditional SPH, accuracy analysis is adopted to point out accuracy behaviors of function and its derivatives when particles are order and disorder distribution. The reason of low accuracy for particle disorder arrangement is founded. Some numerical tests are used for the verification.Secondly, it introduces the improved method of kernel approximation, named K2_SPH. After the error analysis, the orders of accuracy for its function and derivatives are obtained. From numerical tests,the accuracy of K2_SPH can get significant improvement, especially when particles are disorder arrangement or near the boundary domain.Moreover, according to the comparison of other meshless kernel interpolation methods, K2_SPH still has obvious superiority.Thirdly, some typical hydrodynamic models are simulated by SPH and K2_SPH, which including plate flow, standing wave simulation, piston wave making and sloshing wave simulation. According to the comparison of different factors,some characters of SPH and K2_SPH are obtained. K2_SPH can get obviously better results and overcome some shortcomings of SPH, especially in the aspect of some important middle variables.K2_SPH improves the reliability of SPH distinctly.Lastly, K2_SPH still has some limitations for complex free surface simulation, like breaking or overturning flow. So it just adopts traditional SPH in the case of violent free surface problems, which including the cases of dam breaking, boring problem and large amplitude sloshing in liquid container. The purpose of this section wants to investigate the capability of SPH method for complex free surface simulation. During the simulation of liquid sloshing, it adopts the technology of moving coordinate transformation, which is easy to realize the simulation of coupled 2D motion in three freedom degrees.According to comparison of different cases, it gets the superiority of SPH method to simulate strongly non-linear free surface flow. Some shortcomings are also introduced in details,which are very helpful for the further research of SPH.