COMPUTER SIMULATION OF UNSTEADY-STATE MEDIUM MOTION HAVING EQUILIBRIUM PHASE TRANSITION

V. F. Kuropatenko
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1979. No 4. P. 3-12.

      This study considers several issues, encountered while constructing and justifying a compressible multiphase media computational model and simulating such media. A new type of small discontinuties is investigated and its impact on the accuracy of conservation law system numerical integrations is estimated. A single medium equation-of-state with a polymorphic phase transition is given, a method for calculating accurate shock waves is formulated, and calculational results are presented. Point burst problems for one and two phase medium are compared.

T. V. Zabelina, N. I. Leonova, Z. V. Surayeva, A. V. Timonkina
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1979. No 4. P. 13-15.

      The paper describes the structure of programs (URS-OK) which, in combination with the 1-D Complex, support a program package for solving 1-D computational physics problems.

A. F. Nikiforov, V. G. Novikov, V. B. Uvarov
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1979. No 4. P. 16-26.

      A quantum mechanics model is described, which may be used to predict different material properties. Since exchange effects may greatly contribute to thermodynamic functions, a variational law was used to progressively derive an expression for the exchange potential at arbitrary material temperature and density.
      To reduce the computation time, a capability is provided to take into account overlapping strips or unfilled electron states in a quasi-classical approximation. It is shown, that such simplification does not lead to a considerable decrease in calculation accuracy.

A. F. Nikiforov, V. G. Novikov, V. B. Uvarov
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1979. No 4. P. 27-35.

      A material equation-of-state is derived, based on the HFS model, and the conditions for thermodynamic model consistency are obtained. It is shown, that taking into account the exchange effects in wave functions may substantially influence the calculational results at low temperatures and densities, close to normal ones. Comparing the results obtained with those of TFP model indicates that shell effects play an important role and may greatly exceed quantum and exchange corrections.

A. F. Nikiforov, N. Yu. Orlov., V. B. Uvarov
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1979. No 4. P. 36-39.

      The paper compares the results of a light absorption calculation with experimental data on Ar plasma for a temperature of 20.000K and densiltes from 10¹⁷ to 10²¹ atom/cm³. To estimate photoionization cross-sections, a method is proposed for calculating matrix elements with rapidly oscillating wave functions.

G. V. Kovalenko, A. T. Sapozhnikov
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1979. No 4. P. 40-46.

      The derivation of a tabular water equation-of-state for densities of 0-5 g/cm³ and specific energies of 16 MJ/g is considered. The tables are obtained from calculations using equations for water and theoretical models. Thermodynamic quantities derived from the tabular equation-of-state agree well with the well known experiments and theories.

A. T. Sapozhnikov, A. V. Pershina
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1979. No 4. P. 47-56.

      The paper considers the derivation of a metal equation-of-state for a thermodynamic quantities range, which occurs at shock compression and subsequent unloading.
      The equation-of-state includes potential, thermal, and "electron” pressure and energy components, with the associated formulae derived from the well known metal behavior models. The equation parameters were defined by the condition providing an optimal representation of thermal physics data involved in static tests and experimental data on the shock compression of solid and porous metals. Hugoniot adiabats for copper, aluminium, lead, and iron, along with their characteristics in evaporabed and liquid states, are calculated. A satisfactory agreement of our predictions with experiment is indicated.

I. F. Podlivayev
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1979. No 4. P. 57-63.

      Numerical experiments are used to study the feasibility of formulating an inverse problem, which derives an unknown equation-of-state for a barotropic fluid model from plane time-dependent problem solutions with redefined boundary conditions. The calculations resulted in a conclusion showing the posibility of deriving the equation with a moderate accuracy, if some redefining is made.

G. U. Yeliseev
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1979. No 4. P. 64-70.

      A system is proposed for creating table archives of hardly definable functions in the form of FORTRAN subroutines, where digital data is stored in the DATA statement list. To reduce the digital data, approximation spline coefficient should be stored. An efficient algorithm "for natural spline construction is described.
      An example illustrating a program, used to calculate photo ions scattering cross-sections on free electrons, is shown.