Issue N^{o} 3, 1986 
NUMERICAL SIMULATION OF UNSTEADYSTATE FLOWS IN A TWOCOMPONENT HETEROGENEOUS MEDIUM WITH RESPECT TO COMPONENT VELOCITY AND TEMPERATURE NONEQUILIBRIUM
O. V. Buryakov, V. F. Kuropatenko VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 3. P. 39.
We examine a computer model of shock processes in heterogeneous media with respect to component velocity and temperature nonequilibrium. The paper proposes a closed computer model and a numerical method for integrating a system of equations. To ensure a common deformation component pressures are assumed to be locally inequivalent. The method describes the features of shock processes in heterogeneous media (that is multiwave structures, mass component concentration behavior etc.) with a good accuracy.

SMALLPERTURBATION LAGRANGIAN EQUATIONS IN GAS DYNAMICS WITH RESPECT TO MEDIUM HEAT CONDUCTION OR MAGNETIC PROPERTIES G. A. Grishina VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 3. P. 1012.
Lagrangian variables were used to linearize a 3D solution of equations in gas dynamics (with medium heat conduction or magnetic properties included or removed). The basic flow may be both one and twodimensional. Equations for determining small perturbations along the particle path in a basic flow are given in a vectorized form and in generalized Lagrangian variables.

RADIATION TRANSPORT CALCULATIONS FOR LINES WITH THE VOIGT PROFILE V. Ya. Goldin, V. A. Degtyarev VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 3. P. 1319.
For radiation transport in a line with a local thermodynamic equilibrium, an efficient frequency averaging method is tested. For a problem with LTE removed, we propose several methods for combined calculations of radiation transport in lines and level kinetics. These calculations rely upon reducing the transport equation to a diffusionlike system and approximating the transport equation in terms of useful life time (Tapproximation). The methods were tested by computing radiation propagating through a plane cold material layer.

ON SOME EXACT SOLUTIONS FOR A SYSTEM OF ENERGY AND RADIATION TRANSPORT EQUATIONS WITH RESPECT TO SCATTERING V. Yu. Gusev, M. Yu. Kozmanov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 3. P. 2021.
We derive an exact solution for a system of energy and radiation transport equations with respect to scattering, while scattering and absorption coefficients are not proportional. The solution is parametrically given by elementary functions. The method of indefinite functions is used to derive the solution.

MVOK PROGRAM FOR COMPUTING SMALL PERTURBATIONS IN GAS DYNAMICS V. Ya. Bukharova, G. A. Grishina, O. M. Zotova VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 3. P. 2230.
The program is intended to solve multidimensional problems in gas dynamics using small perturbation method. The problem is linearized based on the main 1D solution and linear perturbations are represented as angular variable Fourier series. A numerical procedure is implemented for combined calculations of exact solutions and harmonic amplitudes in multi region problems using the "viscosity cross" scheme. The program is written in FORTRAN within the 1D Complex. The problem formulation and program organization are described. Numerical results are given which are compared to analytical ones.

USING THE KALMAN FILTER FOR UNSTABLE COMPUTATION PROCEDURES V. M. Bobrov, V. M. Kukhtin, F. M. Chekshin VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 3. P. 3134.
The paper shows how to obtain a convergent solution of a linear problem by adding a filtering procedure to the nonstable approximating operator. Several algorithms are discussed for calculating stationary filter gain. For difference schemes approximating a heat conduction equations, numerical results are given which show the method to converge.

A MODIFICATION OF THE GODUNOV DIFFERENCE SCHEME N. Ya. Moiseev VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 3. P. 3543.
The paper considers the Godunov scheme modification which allows to increase smooth solution accuracy while maintaining such useful features as scheme conservatism and monotonicity. Increasing the result accuracies for smooth solutions is obtained by constructing a difference higherorder approximation scheme from the Godunov scheme and the monotonicity is maintained by using a hybrid scheme where weak and strong shock regions are calculated with the Godunov scheme while smooth solution regions use a higherorder approximation. This modification procedure is simple and generalizes to a multidimensional case in a natural way. Scheme capabilities are illustrated by solving test problems having exact solutions.

A PARAMETRIC FAMILY OF ROMB SCHEMES FOR A NONLINEAR HEAT CONDUCTION EQUATION V. M. Pisarev VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 3. P. 4452.
The paper examines a parametric family of ROMB schemes for a nonlinear heat conduction equation. Heat flux approximation at mesh nodes is studied and a parallel is drawn to threepoint schemes. The temperature scheme removed which is identical to the ROMB, when approximating node heat fluxes, is shown (for a uniform mesh) to give a meanharmonic average of an approximate heat conductivity that depends on scheme parameters. New ROMB modifications are developed for solving a nonlinear heat conduction equation and a comparison is made with a number of methods available.

NUMERICAL DATA CORRECTION WITH RESPECT TO A LINEAR CONVERSION SYSTEM RESPONSE TO CALIBRATION SIGNALS V. M. Mikhailov, R. P. Tarasov, A. E. Temkin VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 3. P. 5360.
We consider the correction of data distorted within a conversion system by analyzing a response to signals of known shapes. For the case of shiftinvariant systems we develop numerical correction iteration schemes with a stabilizing operator. For a typical conversion system numerical experiment results are given to show the efficiency of methods under consideration in a rather broad class of applications.

A METHOD FOR FINDING A GENERALIZED SOLUTION WITH AN IMPLICIT DIFFERENCE SCHEME EXEMPLIFIED BY A QUASILINEAR TRANSPORT EQUATION N. N. Bokov, E. G. Glinskikh VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 3. P. 6167.
A quasi linear transport equation is used to exemplify a method for computing large and small discontinuities in an implicit difference scheme. The continuous solution region uses an implicit difference scheme. For a large discontinuity the solution is fitted with respect to the Hugoniot condition. A small discontinuity requires that a continuity condition should be met. The complete system of difference equations is solved by threepoint runs. The resulting difference scheme possesses a property to maintain small discontinuities in initial data, preserves the solution structure, reproduces satisfactorily the solution on a coarse spatial mesh, and converges to an exact solution as the timestep decreases.

SOME EXACT SOLUTIONS FOR A SYSTEM OF EQUATIONS IN RADIATION GAS DYNAMICS M. Yu. Kozmanov, A. Sh. Nurbakov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 3. P. 6870.
We have obtained exact solutions for the radiation propagating through a moving medium with scattering effect removed for specifically chosen initial data, boundary conditions, and absorption coefficient. The radiafion transfer is considered both for a full spectral formulation and for various approximations. The resulting solutions may be used to validate approximate methods.

A DIFFERENCE SCHEME FOR A 1D PROBLEM IN FLUID DYNAMICS A. I. Zhukov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1986. No 3. P. 7177.
The paper considers a family of threepoint explicit difference schemes for numerical integration of D fluid dynamics equations with oneparameter dependence. A parameter is chosen to give the highest accuracy in a smooth region and the profiles, close to monotonous ones, in shock waves.

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