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. No 2. P. 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.

V.G. Morozov, L.V. Dmitrieva, I.I. Karpenko, N.V. Korepova
VANT. Ser.: Mat. Mod. Fiz. Proc. 1999. No 2. P. 12-17.

      A numerical simulation is performed for experiments on detonation wave generation in a TATB explosive with initial density of ρ₀ = 1,91 g/cm³ with short duration pulses, that is at TATB explosive impact by thin films (0,005-0,127 cm) with a small initial density of 1,2 g/cm³. The films were accelerated up to very high speeds (3,4-8,2 km/s) by aluminium foils explosion. Computations were carried out with D codes implementing a method for 2-D time-dependent gasdynamics in Lagrangian variables and a kinetic model for explosive detonation generation, developed under V.G. Morozov management. The model is shown to demonstrate well the main mechanisms of a TATB explosive generation with short duration pulses.

S.A. Stepanenko
VANT. Ser.: Mat. Mod. Fiz. Proc. 1999. No 2. P. 18-23.

      The time complexity estimations are obtained for algorithms implementing a lot of global data exchange operations in multiprocessor environments with various communication topologies. The non-collision exchange probabilities are estimated.

A.M. Vargin, D. Nielsen, A. Skjellum, Yu.G. Bartenev, N.A. Mustaeva, S.A. Firsov, S.N. Egorov
VANT. Ser.: Mat. Mod. Fiz. Proc. 1999. No 2. P. 24-27.

      A study was made of conceptional construction problems and implementation features of parallel libraries executed on various firmware platforms, supporting the most frequently used programming languages and implementing the most general and effective methods for solving sets of equations for a wide range of application problems. The performance data, features and state of the libraries implemented at the moment are given. The perspectives of practical application and development for a given work are considered. The work implemented under four-sided agreement between Lawrence Livermore National Laboratory (LLNL), Intel Inc., Mississippi State University (MSU) and RFNC-VNIIEF on the “Parallel mathematical libraries” project is presented.

S.N. Egorov, A.I. Prokof´ev, E.A. Shuvalov, V.V. Shumilin
VANT. Ser.: Mat. Mod. Fiz. Proc. 1999. No 2. P. 28-30.

      It is reported that a function library for iterative solution of spare linear systems has been created. The library is created under implementation on The Parallel Mathematical Libraries Project on the basis of BLASP library, leaving a wide set of functions for a user to perform various actions with spare matrices.

Yu.G. Bartenev, A.M. Vargin, V.A. Erzunov, N.V. Frolova, V.V. Shumilin, E.B. Shchanikova, V.S. Ovechkin, V.G. Basalov, S.R. Orlov, V.S. Rudkovsky, N.N. Vyskubenko
VANT. Ser.: Mat. Mod. Fiz. Proc. 1999. No 2. P. 31-36.

      The requirements are imposed on construction of successive and parallel BLASP library, resulted from a program model for parallel solution of M(t) x = u(t) equation. The methods for matrix disribution to processes and exchange schemes are studied. The obtained performance is presented.

A.M. Vargin
VANT. Ser.: Mat. Mod. Fiz. Proc. 1999. No 2. P. 37-40.

      A toolkit is presented which is designed on the basis of MPICH system and which constructs, debugs and executes parallel MPI-programs using work user stations under control of Windows 95 and Windows NT operating systems with no use of expensive parallel operational systems. These tools are useful for both those who start constructing first parallel programs and those who want to optimize the work of the existing parallel programs.

A.D. Gadzhiev, V.V. Gadzhieva, S.N. Lebedev, V.N. Pisarev, E.M. Romanova, V.V. Rykovanova, A.A. Shestakov
VANT. Ser.: Mat. Mod. Fiz. Proc. 1999. No 2. P. 41-52.

      The paper deals with FENIKS program system for mathematical simulation of continuum dynamics and its application for studying the evolution of a single-mode geometric perturbation, arising on the plane target surface under the influence of laser radiation. Numerical calculations on the perturbation investigation were performed with regard to hydrodynamics and photon transport in approximation of radiant heat conduction or spectral diffusion. To calibrate computations, comparative computations of one-dimensional problems using ERA program system with regard to photon transport in spectral diffusion approximation were performed as well as comparative calculations of 2-D problems on TIGR system with regard to photon transport in the radiant heat conduction.