ANALYTICAL AND NUMERICAL STUDY OF RALEIGHTAYLOR INSTABILITY FOR HYDRODYNAMIC PROBLEMS IN SHELL APPROXIMATION IN 3D FORMULATION
F.A. Pletenev, Yu.A. Rezchikova VANT. Ser.: Mat. Mod. Fiz. Proc 1999. Вып.2. С. 311.
The work is dedicated to the construction and study of numerical models for solving 3D gas dynamic problems in shell approximation. The actuality of a shell model development is concerned with need for both solving the problems of a thinwall construction dynamics and reducing emergency stops in Lagrangian methods at heavy pinches in physical domains. The models developed by Ott and Manheimer for studying nonlinear behaviour of RaleighTaylor instability of an infinite thin layer in 3D case were used in the work. Numerical schemes for a thin layer motion in a 3D gas dynamic approximation using Lagrangian coordinates are presented. Besides a difference model a thinlayer model is described based on the method of decomposition into harmonics. Dispersive relations for both models are obtained. Approximational equations are constructed. The computations are presented for RaleighTaylor 3D perturbation evolution resulting from acceleration of thin layers by constant pressure. The models proposed for computing 3D RaleighTaylor instability showed their serviceability. The study made for perturbation evolution can be used to set up 3D computations for thinwall system dynamics and to carry out various experiments in this field.
