Numerical Simulation of Two-Dimensional Flows by the Free-Lagrangian Method

摘要

The development, realization, and verification of a purely Lagrangian,conservative free-Lagrangian method are described. The term 'purely Lagrangian' means that the mass of particles is not changed; no mass, momentum, and energy exchange appears between particles; no interpolation or smoothing procedures are used; and the cell connected with a particle contains only one material (there are non-'mixed' cells). In the method, the network structure is determined by the Dirichlet tesselations of the computational domain. It is shown by a computational experiment that the volume of a Dirichlet cell varies more smoothly than that of comparable approaches when the structure of the grid changes. The continuity of the volume determines, for Lagrangian methods, the density continuity of the given particle. Another important property of the Dirichlet volume is that its derivatives, with respect to particle coordinates, are likewise continuous. These derivatives appear in the difference equations, so that acceleration, velocity, internal energy, and pressure are continuous. The conservative difference scheme is obtained by using the method of support operators. The approximation property of the constructed difference scheme is investigated. Some approaches to the treatment of free boundaries are described. Results of computation are presented for some two dimensional problems.