METHODS OF NUMERICAL MODELING OF 2D NONSTATIONARY GASDYNAMIC FLOW WITH HEAT CONDUCTION IN THREE-TEMPERATURE APPROACH

A. V. Zabrodin, G. P. Prokopov
VANT. Ser. Mat. Mod. Fiz. Proc. 1998. No 3. P. 3-16.

      The medium (plasma) is described as a gas with unit density and common velocity of particles. Temperatures, pressures and inner energies of ions, electrons and photons are different in each point of space and time.
      Existing methods for numerical calculation of 2D equations of dynamics of heat conduction gas in regions of complicated shape is generalized in case of such a medium. One saves its basis conceptually and algorithmically: the well known Godunov scheme with Riemann problem is generalized for heat conduction gas.

A. A. Bazin, G. I. Skidan, B. P. Tikhomirov
VANT. Ser. Mat. Mod. Fiz. Proc. 1998. No 3. P. 17-23.

      The stability of the method of separate computation by regions is considered for two diffusion and equation integration algorithms. The stability condition is discussed for the algorithm in which a radiation flux is transferred from the diffusion region into the vacuum one and temperature — from the vacuum region into the diffusion one. The conditionlessly stable algorithm for setting up exchangable boundary conditions is given, consisting in one-side flux transmission. Computed data of two model problems having an exact analytical solution are presented.

S. M. Bakhrakh, Yu. E. Kornilov
VANT. Ser. Mat. Mod. Fiz. Proc. 1998. No 3. P. 24-26.

      The problem on Raleigh-Taylor instability of the interface between fluid and elastic body has been analyzed. An analytic solution is obtained in linear approximation for the case of the uniform and pulsed acceleration joint effect. The solution obtained is not a simple superposition of solutions for the cases of either uniform or pulsed accelerations. On the contrary our solution contains these particular cases. The relationship of the perturbation amplitude to time for the water-rubber interface is analyzed by the way of example assuming the ideal character of both media.

A. S. Kozlovskikh, D. V. Neuvazhaev
VANT. Ser. Mat. Mod. Fiz. Proc. 1998. No 3. P. 27-33.

      The equation in the heterogeneity factor has been analyzed in the area of turbulent mixing (TM) in large Reynold and small Mach approximation. The self-similar solution is given for the LV-model with TM area constant turbulent diffusion factor.

A. A. Basin, G. I. Skidan, B. P. Tikhomirov, E. N. Tikhomirova
VANT. Ser. Mat. Mod. Fiz. Proc. 1998. No 3. P. 34-40.

      The paper deals with calculation method for heat transfer problems based on diffusion and vacuum approximations. Stable exchange boundary conditions are introduced for solution conjugation of the nonlinear heat conduction equation (or radiation diffusion equation) with integral equation for heat exchange of radiation on the opacity boundary. The boundary conditions of diffusion type are discussed, a simple method for diffusion flux restriction is proposed.
      An example of a radiant heat exchange problem with analytical solution is constructed; the accuracy of the model problem calculation is estimated with this problem. Computed data for a model problem of temperature distribution on box and container walls at fire are presented.

A. A. Basin, V. V. Vatulin, Yu. A. Dement’ev, V. F. Mironova, G. I. Skidan, B. P. Tikhomirov, E. N. Tikhomirova
VANT. Ser. Mat. Mod. Fiz. Proc. 1998. No 3. P. 41-45.

      One of the possible options is discussed for the medium motion within the diffusion-vacuum model for radiant energy transfer calculation in the optically nonhomogeneous 2D and 3D systems.
      2D computed data are given for X-ray field in the laser cylindrical targets of small diameter. The radiation field symmetry on the capsule surface of the heavy-ion cylindrical target is considered.

Yu. M. Kovalev
VANT. Ser. Mat. Mod. Fiz. Proc. 1998. No 3. P. 46-52.

      The choice is justified of a time averaging for heterogeneous media mechanics with small bulk of condensed phase. The identity of mass averages and weighted averages (with averaging according to A. Favre) is proved.