ON RUNNING RATIOS

I. D. Sofronov
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1982. No 2. P. 3-13.

      The behavior of running ratios for a 1-D heat conduction equation depending on coefficients associated with a boundary conditions flow is examined. Some cases are shown where the run method does not lead to a desired solution. Several conditions are established to avoid these cases.

A. V. Zabrodin, A. V. Pekarchuk
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1982. No 2. P. 14-22.

      A nonlinear heat conduction equation integration algorithm for the case of two space variables is presented. Time step calculation is divided into two stages. The first, or intermediate stage, solves a linearized equation using an implicit scheme and finds the temperature distribution for t + ατ (0,5 ≤ α ≤ 1). The operator conversion is made by means of an iteration loop, containing four-directional runs with iteratin parameters selection. The second stage defines a final temperature distribution for t + τ using the conservation law. Heat flux values are computed from the temperature distribution in the first stage. Examples illustrating numerical calculations are given.

N. N .Anuchina, V. N. Ogibina
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1982. No 2. P. 23-31.

      The results of a numerical simulation describing a fully grown gravitational turbulence are presented. The turbulent motion is assumed to be described by two space variables hydrodynamic time-dependent equations for inviscid non-conducting gases. The solution is obtaind with a difference "particle-in-cel1" method. Some problems having self-similar solutios obtained using semiempirical turbulent diffusion theory are examined. A comparison between numerical results and analyt ie- solut ions is made.

G. P. Prokopov
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1982. No 2. P. 32-40.

      The paper studies an iteration algorithm used to compute a configuration encountered when solving the Riemann problem at an interface between two media governed by given two-term equations of state having their own parameters on either interface side, or in the case where one of the media is porous (or both are) while being governed by two-term equations of state, after the pores were shock-collapsed. Several factors associated with initial approximation setting and removing the features that may considerably slow down the iteration convergence, are examined. Evaluations are made to assure achieving a user-specified accuracy.

N. A. Ismailova, V. Ye. Konclrashov
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1982. No 2. P. 41-48.

      This paper represents the first portion of efforts aimed at examining the impact of boundary conditions, set as a linear flux/temperature combination, on a two-layer difference scheme stability which approximates a 1-D linear heat conduction equation. Heat conductivity, space step, and upper layer weight are assumed to be variable quantities. Several spectral system representations are given, spectral system running ratios are estimated, and all transition matrix eigenvalues are proved to be always real.

V. Yu. Melzas
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1982. No 2. P. 49-58.

      The Godunov Scheme stability is proved for region-by-region computation with different time steps. Jump size on the contact boundary is evaluated for acoustic equations and a linear solution. It is shown, that the scheme jump size for splitting computation does not exceed that of a conventional scheme. Some examples of numerical computation with splitting scheme both for linear and nonlinear cases are presented.