GODUNOV METHOD MODIFICATION FOR EULERIAN TIME-INDEPENDENT EQUATIONS

I.S. Menshоv
VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 3-13.

      The paper considers a classical self-similar problem for the interaction of two homogeneous supersonic gas flows which is generalized to the case where the flows are nonhamogeneous that is gasdynamic parameter distributions are arbitrary and, in general, nonfixed. An explicit analytic solution is locally derived for this non-self-similar problem in the small vicinity of the flow interaction profile which is then used to increase the Godunov scheme accuracy for gasdynamic time-independent equations.

Yu.A. Bondarenko, B.L.Vогоnin, V.V. Gоrev, V.I. De1оv, E.N. Zubоv, Yu.M. Matveev, A.I. Mоrenко, S.S. Sоко1оv, V.E. Shemarulin
VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 14-20.

      A description of four test problems is proposed intended for testing methods and programs for numerical 2-D heat conduction calculations.

Yu.A. Bondarenko
VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 21-23.

      For a multilayer medium consisting of various materials with their boundaries being straight lines, a method is described to derive exact solutions for the quasllinear diffusion equation: where the constants c_i, v_i and æ_i, differ for each material i while being interrelated. Well-known 1-D solutions are used such as the solution for a heat wave moving with a constant velocity through zero background. Temperature and flow equivalence requirements for the boundary between different materials imply some constraints on parameters c_i, v_i and æ_i resulting from the angle between the heat wave front and material boundary and also from the heat wave velocity. A specific problem is cited to be used as a test one.

N.Yu. Bакaуev
VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 24-28.

      Inequalities are obtained a priori which represent instability for one class of splitted difference schemes in Banach spaces. The theory developed is used to study stability in space norms L_ph I ≤ p ≤ ∞ of splitted difference schemes for a 2-D heat conduction equation.

V.V. Belоv, V.G. Niкоlaev
VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 29-31.

      A numerical method is developed for solving equations which describe fiber stretch processes for a quasi-one-dlmensional case. Newton iteration method is used to resolve the nonlinearity of equations. Our method relies upon ADI algorithm for linear systems with shaped matrices.

V.V. Goncharov, S.I. Коva1уоv, Yu.V. Kоsse, S.Yu. Malкоv
VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 32-36.

      This paper examinee electrodynamic and radioactive effect of penetrating radiation on a dielectric cylinder structure represented as an infinite cylinder with a filling material. Electric breakdowns are shown to occur in the structure shell due to the above effects. A method is presented which allows to estimate potential and current distributions along the inner shell surface, a numerical solution is derived using finite element method. Numerical results for a specific structure are used to determine possible location of a breakdown due to radiation which was represented by a flux of neutral hydrogen atoms. A condition is defined for breakdown occurrence in a cylindrical dielectric shell.

V.P. Vagin, V.V. Zhakhоvsку, М.P. Ivanоv, V.V. Saviсhev
VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 37-41.

      Experimental and theoretical studies were performed to investigate temperature fields in samples of phenol-phormaldehyde-resin- based glass plastic Irradiated by a continuous 30 Mev proton beam at a rate of 10¹⁴ particles/cm-sec. A model is constructed which allows to describe the temperature evolution in glass plastic samples with thermal material destruction, highly nonlinear ther- mophysical coefficients and energy output variations. Experiments agree well with calculations which permit to conclude that the radiation component of the phenol-phormaldehyde decomposition is negligible under above conditions.

L.P. Priadкo
VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 42-45.

      Electromagnetic radiation and surface current excitation laws are Investigated for a powerful incident x-ray pulse impacting the target surface in the vacuum. The motion of knocked-on photoelectrons is determined both by the electrostatic field and the emitted wave field. The radiation field is shown to dominate for grazing Incidence of x-rays. Such situation is interesting from a general physics point of view as it provides an example of system with the motion being determined by the radiation brake force. A simple analytical model is presented for this case.

V.N. Maгкelоv
VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 46-50.

      A computer model is proposed for a phenomenological thermodynamic equation describing a porous medium allowing thermal stress relaxation when an expansion Into voids occurs.
      For Incomplete compaction region, pressures are described based on a volume plasticity model with a variable volume compaction modulus for a porous medium. For a complete compaction region and relaxation, we use the well-known equation of state for solids which includes material vaporisation. Stress deviator components are computed using shear plasticity model with Tresk-Sen-Venan yield strength. The model of a porous medium gives a three-wave configuration for a shook in a low pressure region.
      Experiments and predictions are compared for shook compression of the PS-1 foam. Relaxation dynamics of thermal stresses is calculated for KT-11.

N.Yu. Baкaуev
VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 51-53.

      Coersion inequalities are established for Runge-Kutta difference scheme stability for parabolic equations.

V.P. Gоrelоv, A.N. Grebenniкоv, G.O. Parafontov
VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 54-57.

      Numerical comparison is performed for three calculational procedures using consecutive approximations of K_ef The studies allowed to conclude that the forward procedure is efficient and cost-effective. This is recommended to use in 2-D and 3-0 calculations of critical parameters.

V.M. Melniкоv
VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 58-62.

      Cost-efficient splitting schemes are proposed for a Maxwell system with a retard time τ (τ is the time elapsed from electromagnetic wave arrival to a given point) which does not refer to the Cauchy- Kovalevskaya class. A typical problem is used to study the scheme properties which were tested by numerical calculations. Real scheme characteristics (computation accuracy and time) are compared with other parameters used in practice.