The Study Of Lagrange Method And Rezoning Algorithm

The purpose of this dissertation is to study the Lagrangian method and conservative rezonning algorithm.Finite volume scheme is used for Lagrangian equations of hydrodynamics. Because of the pressure gradients' influence upon velocities and energy, Computational scheme is proposed for momentum equation on two control volumes in order to suspend the time when the mesh becomes distorted.Based on the idea of subordinate meshes, we bring forward a new method of weighted volume which is used for constructing linear interpolation polynomials. Besides, According to the ENO interpolation on unstructured grids, A class of linear interpolation polynomial is developed on irregular quadrilateral grids and allows very small oscillation.Program in Fortran is given for a remapping algorithm developed by CaiQingdong. Besides, We give another conservative remapping algorithm in allusion to the difficulty of integrating the known density distribution in the old mesh over the cell volume. The new mesh is subdivided in order to calculate the densities of new smaller meshes. Then densities of the new mesh are known accordingly and high accuracy remapping is finished. Finally, Series of numerical experiments are made with ALE method and the results show that the method is effective.