Study On Incompressible Free-surface Flow By SPH

Incompressible free-surface flow mainly points to the flow which has a interface with atmosphere, and its physical parameters are disconnected or discontiguous at interface. This kind of problems extensively exist in shipping and ocean engineering, hydraulic engineering, mechanical engineering, oil and chemical engineering , and also civil engineering. So, it has important meaning in researching on incompressible free-surface flow by SPH.SPH belongs to particle method which is completely Lagrange describing and has no grid. The advantages of SPH are as follows: simulating liquid convection by particles directly to eliminate numerical fluctuation at free interface, to guarantee the accuracy of the tracing of free-surface; grids unnecessary avoid grid distortion and reconstruction; simulating the fliud problem of significant free-surface transformation. By far, the investigation of simulating free-surface flow by SPH which made by other researchers has obtained great progress and still has a lot of disadvantages. In this thesis, some researches are done to improve the application of the method in free-surface flow simulation.On the side of basic theory in the thesis, firstly, the basic idea of SPH, the integral expression method of a function and its one-order and two-order differential coefficient by SPH, and the method approximating to a function by SPH particles are particularly discussed. Secondly, the basic equations of SPH method are founded. Thirdly, some basic conceptions such as smoothed function, support field and influence field are analysised. Lastly, the principle and the calculating formula of the modified SPH method(MSPH) are expounded. On the base of the work above and the conversation of mass, momentum, and energy, the Lagrange type liquid movement N-S equations under Descartes coordinate system, cylinder coordinate system, and sphere coordinate system are set up respectively. And by dispersing N-S equations in space according to SPH method, the SPH control equations which can be applied to generalized hydrokinetics under different coordinate system are entirely established.On the base of 2-D hydrokinetics SPH control equations, the corelative techniques of SPH are investigated when the method is used to simulating incompressible free-surface flow which has no impact movement in flow. Thereinto, the method of initial particles disposal and the symmetry of interaction between particles are discussed for the first time, and an idea combining boundary condition disposal method in SPH and boundary condition disposal method in common liquid movement numerical simulation is bringed forward. The validity of numerical technique researched is proved by liquid sloshing simulation.According to the characteristic of feeble impact free-surface flow and based on the MSPH method, the modified 2-D hydrokinetics control equation of SPH is established, and also the interrelated numerical techniques of SPH are studied. The rationality of SPH method is validated by dam breaking numerical simulation.Further researches on numerical simulation of strong impact free-surface flow by SPH are done. Firstly, SPH hydrokinetics control equations with Riemann solution are introduced to solve the discontinuity of numerical solution, and then interrelated numerical techniques of SPH are studied as follows: a new method of how to search the free-surface particles is determined; tension instability and artificial stress are considered for the first time. Finally, through the simulation of a drop impacting free liquid surface by SPH, the validity of the equations and numerical techniques in the problem of strong impact free-surface flow is testified. Besides, the simulation of a drop impacting free liquid surface by SPH is carried out for the first time.