COMPUTING THERMODYNAMIC FUNCTIONS IN TWO-PHASE LIQUID-VAPOUR REGION USING SPLINE-APPROXIMATION

L.F. Gudаrenко, V.A. Zherebtsоv
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 1. P. 3-7.

      Computing method for thermodynamic functions in two-phase liquid-vapour region using iterationless algorithms is presented. The calculations require thermodynamic function values specified at two-phase region boundaries and approximation of them by polynomial values- cubic and quadratic. The above method allows to compute thermodynamic function values together with their derivatives with respect to any of the following three pairs of variables: density - temperature, density - pressure, density-energy.

V.T. Zhuкоv, A.V. Zabrоdin, V.S. Imshennik, O.B. Feodoritova
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 1. P. 8-18.

      Numerical and analytical investigations of HIF (heavy ion fusion) target dynamics are carried out. The influence of perturbations on compression process is investigated. A special attention is given to the Rayleigh-Taylor instability. The calculations are based on difference discretization of 2-D time-dependent equations of heat-conducting gas dynamics. The presentation of compression process of target and significance of little perturbations in this process is obtained. The small-scale perturbations (about thickness of shells) are described with the crude analytical approximations.

О.B. Кhairullina
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 1. P. 19-25.

      New variant of method and "MOPS-2a" program for generation of optimal curvilinear block-structured grids in multiply-connected two-dimensional regions of complex geometries is described. This variant permits to reduce essentially the volume of input information, to automatize the overlapping of blocks. For all main topologies the results of computations are given.

M.I. Avramenko, E.S. Andreev, A.P. Vasil´ev, V.Yu. Gusev, M.Yu. Kоzmanоv, V.F. Kuropatenko, E.B. Raсhilоv, V.A. Simonenкo
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 1. P. 26-31.

      The paper describes the special features of ECOL, TREC, RIM codes destined for simulation of impurity propagation in atmosphere.
      Some numerical results are given.

O.V. Butneva, V.A. Shumilin
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 1. P. 32-35.

      Internal boundary condition influence upon the number of iterations in solution of time- dependent neutron transport equation is discussed. Internal boundary condition iterations coincide with collision integral iterations. The method of correction is used for convergence acceleration.
      Iteration convergence speed is numerically studied in solution of transport equation on subdomains for 1-D and 2-D cases. A comparison with one-domain calculations is performed.

G.P. Prokopov
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 1. P. 36-44.

      A non-interacting system of initial data preprocessing is described for 2-D regular mesh calculation in single-link and multi-link domains. Calculated domain contour is assumed to be specified by reference point system. The algorithms are presented for discrete reproduction of the arcs, connecting the neighbouring reference points. The prototype of calculated domain is automatically formed on node number plane in difference mesh. It is divided then into blocks of simple structure. The task monitoring and initial data preprocessing facilities for the following mesh calculations are given.

V.A. Svidinsky
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 1. P. 45-51.

      The conception of the through-out projection numerical method based on continuous argument functions is presented. Taking as a basis the wave nature of solutions for a hyperbolic system so called wave variables that are most adequate to each wave type are involved. Numerical method is based on analytical description of solution evolution as approximate splitting on superposition of different waves. Thus obtained standard solution of complex structure is simplified by the projection operator taking into account conservative variables balances. The technology of CW-method is illustrated for a linear equation and a linear system. It is shown that the numerical solution coincides with exact solution for certain conditions.

V.A. Svidinskу
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 1. P. 52-57.

      Developing the CW-method technology on nonlinear problems is considered. Consideration of heterogeneity of wave velocity is demonstrated on the nonlinear scalar equation. Consideration of nonlinear connections between wave and conservative variables is illustrated for the model system.

V.V. Vyshinsky, S.A. Kravchenko, A.M. Sоrokin
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 1. P. 58-67.

      Aerodynamic calculation of transonic flow over 2-body system is studied. The effect of calculated mesh topology and boundary constraints statement concerned with it over accuracy of results, physical properties and obtained solution conduct is examplified using one and the same boundary problem algorithm to time-dependent Eulerian equation. The paper illustrates the possibility of different approaches towards mesh selection in solving of aerodynamic problems. The comparison of obtained numerical solutions with experiments allowed to show specialties of various approaches to discretization of domains with intricate curvilinear boundaries.

L.G. Strakhovskaya, R.P. Fedorenko/
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 1. P. 68-77.

      Approximation method for Lame equations on a mesh adapted to a region geometry is presented: boundaries cutting the region into zones with different physical properties run along the mesh cell boundaries. Mesh cells at a x, у-plane are irregular form quadrangles, a mesh along z is specified by a table. Seidel method with multimesh acceleration is suggested for solving difference equations. Convergence iteration data and accuracy analysis for approximate solutions are given.

R.N. Antоnоva, G.P. Prokopov
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 1. P. 78-84.

      The possibility of formula collection extension for difference mesh generation in quadrangular region, specified by discrete node set in a contour with predefined matching using transfinite interpolation is studied. The examples are included when the invalenty requirement for feasible mapping isn´t met even in the simpliest cases.