SATURN TECHNIQUE FOR NUMERICAL SOLUTION OF 3-D TIME-DEPENDENT TRANSPORT EQUATION

A.V. Aleкseev, V.V. Evdokimov, R.M. Shagaliev
VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 3-8.

      A computational technique for numerical solution of 3-D time-dependent transport equation in classical cylinder system of coordinates on nonorthogonal spatial grids is formulated.
      The finite-difference approximation for the transport equation is developed according to the scheme with additional relations. The scheme formed is conservative, the corresponding difference transport operator is of the packaged-delta form. For the case when the right-hand side is known the cost-efficient method for solving the grid-equation system based on the running computation idea is formulated. In the general case when the right-hand side is unknown the suggested algorithm is used in combination with simple iteration method and simple iteration convergence acceleration methods.
      The method suggested allows an efficient parallelization in several directions, which is critical for multiprocessor implementation.

V.E. Shemarulin
VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 9-15.

      A sufficient point transformation condition is derived for contact symmetries within a special class of second-order quasilinear equations with three independent variables. A simple criterion is found for variational nature of symmetries for Monge-Amper equations and second- order quasilinear equations that are Euler-Lagraage equations for a variational problem. The results obtained allowed to evaluate the contact symmetries and conservation laws for equations that result from the systems describing vortex-free steady-state isentropic 3-D and 2-D unsteady plane and symmetric flows of polytropic gas. Group classification is made for these equations regarding к parameter that represents the gas adiabatic index for к > 1.

G.N. Pоtetуunко
VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 16-21.

      The problem of heavy charged secondary particle motion is considered within the kinetic theory of ion motion through a solid, based on Boltzmann equation in nonstationary formulation; the particles are generated in a plane semi-infinite target as a result of some primary radiation. The consideration is oriented to energies corresponding to the maximum of material electron deceleration level or to those which are somewhat lower where the electron component dominates the deceleration process.

T.A. Bychenkov
VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 22-25.

      Correctness (hyperbolic nature) of elastic-plastic medium model with respect to friability using an associated flow law is studied. The paper gives mathematically correct form of elastic- plastic dynamic equations for isotropic medium deformation which allows to take into account shearing stress relaxation kinetics, dilatancy, anisotropic cracking. The explicit difference scheme stability conditions according to von Neumann conditions are obtained.

V.Yu. Meltzas, G.F. Portnyagina, V.F. Sоlоviоv
VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 26-31.

      Godunov method was used to develop a computational technique for gas flows through fixed lattice-type shields allowing severed, times altenuation of shock wave intensities. A model of "frozen" gas suspension (the lattice nodes are assumed to be fixed, gas/node heat exchange is neglected), the lattice volume content and perforation degree are Included. 1-D computation results are given for shock propagation through the duet medium, across the layer of meshes differing in boundary conditions and 2-D computation data on the attenuation of explosive effect on cylinder vessel walls where lattice- type shields are placed.

V.A. Svidinsку
VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 32-40.

      Application of conservative difference method for the problem of propagation of a steady square wave is considered. It Is analytically shown for waves with front speed Independent on the discontinuities intensity that Godunov type monotonized schemes must give local disbalance of conservative variables within the wave front. Satisfaction of total balance in the computation region results in emanation of side waves by the basic front that distorts the Initial wave configuration. Calculation remits for model problems are presented: the gasdynamic contact discontinuity and the wave which simulates a transverse wave in a thread.

G.P. Simоnоv
VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 41-46.

      Some numerical algorithms are studied for thin liquid behavior in terms of spherical motion symmetry conservation on a 2-D mesh where it must take place as given bу the problem physics. Sane similar features are indicated for rotational shell schemes generation within the thin shell model and continuum approximation. These were used to generate a scheme for 2-D Lagrange gets dynamics with the scheme retaining the spherical motion symmetry even on angular nonuniform mesh (when determining the accelerations) and fully conservative in the case of spherical-symmetry motion on a 2-D uniform mesh. Initially the accelerations are at the centers of all sides and further they are overaged to the nodes.

A.A. Sheatakоv
VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 47-53.

      The paper formulates and proves the maximum/minimum principle for radiant energy transport on P₁- approximation using Romb difference scheme. Unconditionally stable difference schemes are studied in parameter space of the two-parameter Romb family. It is shown that unconditionally stable difference schemes in grid norms of С and L₂ spaces оan be selected from the Romb family.

E.G. Vasina, Yu.A. Dementiev, I.D. Sоfrоnov
VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 54-58.

      The method is intended for 3-D nonstationary radiant energy transport calculations including isentropic scattering, absorption and equilibrium radiation. Strict restrictions are introduced for the fixed time-step size and typical photon path lengths within the fixed all of a spatial grid. These allow to oatoh physical process and mesh distributions. The well known physical relations (Bouguer and Kirckhoff laws. Shauder principle, Lambert´s cosine law for surface radiation) are used to derive approximate equations. The approximation accuracy is studied for the corresponding integrodlfferential equations. The scheme and approximate solution properties are discussed.

E.N. Donskoy
VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 59-63.

      A method is discribed for calculating the bremsstrahlung. Data for the full backword and forward yield for bremsstrahlung and characteristic radiation are given as well as for electrons emitted from the tungsten target of optimal thickness. The incident electron energy range varies from 100 to 600 keV.

V.A. Andrоnоv, A.N. Razin
VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 64-69.

      The paper is devoted to the description of some difference algorithms for numerical simulation of environment problems. The model includes Havier-Stokes equations for background wind components. The impurity transfer is modeled with diffusion and convection equation. Discrete approximation generation and numerical method selection are discussed. Some computational results are given.

A.S. Shvedоv
VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 70-76.

      Multizone procedure for solution of spatial inltlal-boundary problems for the equations of gas dynamics in domains with moving boundaries is described. A method for creation of programs for parallel computers based on those for sequential computers is suggested. Realization of this method for the gasdynamic procedure is shown.

G.V. Zhаrоva, Yu.V. Yanilкin
VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 77-81.

      The paper describes the algorithm for material pressure alignment in mixed cells. The algorithm was developed within EGAK complex for 2-D gas dynamic flow calculations in Eulerian variables. Methodical results are presented.

V.S. Kholushkin
VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 82-89.

      A basic access procedure package for teleprocessing on ES computer is described. The basic access procedure package is considered to be a software tool for multiterminal and multifunctional interactive systems on ES computers.

V.A. Andrоnоv, M.V. Artamonov, S.M. Bakhrakh, S.V. Veliсhко, S.P. Egоrshin, A.A. Kuznechikhia, A.N. Razin, V.F. Spiridonov, Yu.G. Fedоrоva
VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 90-96.

      The paper presents the implementation practices for axisymmetric gas-dynamic flows in heterogeneous medium; the calculations run on STMD PS-2100 computer. The LEGAK method was previously implemented on BESM-6 and ES-1G66. When porting the method to a SIMD multiprocessor only those modifications were made that are needed for a more efficient algorithm parallelization. The main algorithms are given and the organizational code structure is presented for SIMD architectures.

V.A. Ogorodnikov, A.A. Sadovoy, V.N. Sofronov, T.S. Tyunkin
VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 97-101.

      Experimental and theoretical data are presented for burst- driven implosion of cylindrical shells in the deformation rate range varying from 10³ to 10⁶ s^-1.

E.A. Zabrodina, M.D. Churasоv
VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 102-104.

      Implosion and detonation combustion of cylinder heavy-ion fusion DT-target are considered. The thermonuclear gain, G = 16, is calculated with energy input scale E₀ ≈ 100 MJ and thermal insulation (H_0,z ≈ 10⁵ oersted). Certain estimates are also obtained from 1-D gas-dynamic calculations and hydraulic approximation.

M.V. Sokolovsky, M.D. Churazоv
VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 105-110.

      A hydraulic approximation technique is used to consider the detonation burning of a D_0,9³He_0,1 cord with ρ R = 0,05 g/cm² in a multilayer magnetohydrodynamic target. Magnetic heat insulation, magnetic confinement and inertial shell properties are used to ensure the burning.
      The heavy-ion driver is assumed to be able to create necessary Initial conditions for a desired burning mode. The energy contribution scale is E₀~10+100 MJ.
      This work is an, introduction to more strict and more detailed studies of magnetohydrodynamic heavy ion fusion target capabilities for thermonuclear burning.