Numerical Method Research And Application In A Modified MLSPH Method

Smoothed Particle Hydrodynamics (SPH) method is a pure meshless Lagrangian technique which is appealing as a new numerical method used to solve the problems with high velocity and large deformation. The advantages of SPH are:(1)only nodal data are necessary;(2) back-ground grid does not be needed and so the severe problems always associated with mesh distortion in the Lagrangian grid-based methods can be avoided. However, the low computational accuracy at the boundary and the tensile instability are exited, when SPH method is used to solve the solid mechanics'problems. Non-physical phenomena of the particles aggregation appears in tensile state. In order to improve the tensile instability, the Moving-Least-Squares interpolant method is applied to the SPH method, which evolves Moving Least Squares Particle Hydrodynamics (MLSPH) method.This paper is focused on the study of MLSPH methods. The main works in the paper are:Firstly, 1D MLSPH program and 2D MLSPH program are developed on the basic of the theory of the MLSPH method. The effectivity of the programs is verified by patch test. Then the stability of the method is investigated, and numerical simulation of Swegle disturbing test is applied, which shows that MLSPH method is more stable than SPH method. Meanwhile, some numerical aspects such as artificial viscosity, variable smoothing length, nearest neighbor particle searching algorithms are discussed.Secondly, the shortcoming of MLSPH method are investigated in detail, and some effective measures are proposed. Three different forms of discrete equations are given through the introduction of the boundary fluxes, and the conservation of them are discussed. The leaping search method is presented to enhance the efficiency of MLSPH method, the effectivity of this method and the program are verified by some numerical tests.Finally, Then numerical example with shock tube problem is satisfactory by MLSPH method.Some problems with stretching are investigated by modified MLSPH method, which get much better result. Compared with SPH method, the simulated results show that MLSPH method can improve the tension instability of SPH method effectively, and the efficiency of MLSPH method is enhanced by leaping search method.