ANALYTICAL AND NUMERICAL STUDY OF RALEIGH-TAYLOR INSTABILITY FOR HYDRODYNAMIC PROBLEMS IN SHELL APPROXIMATION IN 3-D FORMULATION

F.A. Pletenev, Yu.A. Rezchikova
VANT. Ser.: Mat. Mod. Fiz. Proc 1999. Вып.2. С. 3-11.

      The work is dedicated to the construction and study of numerical models for solving 3-D gas dynamic problems in shell approximation. The actuality of a shell model development is concerned with need for both solving the problems of a thin-wall 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 Raleigh-Taylor instability of an infinite thin layer in 3-D case were used in the work. Numerical schemes for a thin layer motion in a 3-D gas dynamic approximation using Lagrangian coordinates are presented. Besides a difference model a thin-layer 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 Raleigh-Taylor 3-D perturbation evolution resulting from acceleration of thin layers by constant pressure.
      The models proposed for computing 3-D Raleigh-Taylor instability showed their serviceability. The study made for perturbation evolution can be used to set up 3-D computations for thin-wall system dynamics and to carry out various experiments in this field.