Calculation Sph Method And Mlsph Method, Research In Fluid Mechanics

This thesis is focused on the study of meshless methods, in particular, of the SPH and MLSPH methods. When meshless methods are applied in multifluid computations, spurious oscillations often appear in interfaces of different materials. The aim of this thesis is to give some approaches to eliminate such oscillations.Firstly, the SPH and MLSPH methods are introduced briefly, and spurious oscillations are described and analyzed numerically. A detailed discussion on the features of MLS, and the different treatments of the integral and boundary terms in the MLSPH method is given.Secondly, three approaches are presented to eliminate the spurious oscillations of the MLSPH method in the vicinity of interfaces: 1. Domain decomposition computation, which resolves the one-dimensional shock tube problem well, but is not easy to extend to two dimensions, since it not only makes the construction of Riemann problem more difficult, but also is computationally more expansive and complex; 2. Artificial heat flux (added in the energy equation), which works well only for weak shock waves; 3. Meshless MUSCL scheme, which resolves shock tube problems well and is easy to extend to higher dimensions.Finally, the MUSCL-SPH and MUSCL-MLSPH schemes are compared numerically using one-dimensional shock tube problems. In view of computational efficiency, we have chosen the MUSCL-SPH scheme for the simulation of two-dimensional problems and therefore give a 2-D MUSCL-SPH scheme. Moreover, the ways of determining neighboring particles, uniform distributing particles and dealing with the boundary of the meshless MUSCL schemes in two dimensions, are proposed. Several numerical tests with large distortion are given which demonstrate the (potential) efficiency and validation of the meshless MUSCL schemes.