Issue No 3, 1995
NUMERICAL METHOD FOR THE CALCULATION OF ELECTROMAGNETIC FIELDS IN QUASI-STATIC EMP PHASE OF THE CONTACT NUCLEAR EXPLOSION
A. I. Golubev, N. A. Ismailova
VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 3. P. 3-8.
A numerical method is described for the evaluation of electromagnetic fields in quasistatic evolution phase of EMP generated big contact nuclear explosion. The evaluation of fields in this phase reduces to the solution of Poisson equation for the potential of the electric field on the infinite domain containing air-soil interface.
A new boundary condition is proposed for the potential of the soil computational boundary allowing to minimize the domain size.
The Poisson equation is solved with the finite difference method. The potential grid values are calculated with the iterative method of variable directions using the “pre-alignment” of the difference equation coefficients. The way is shown how to choose the iterative parameter allowing to optimize the number of iterations required to achieve the desired accuracy.
|EQUATION OF STATE FOR GRAPHITE AND DIAMOND
A. H. Averin, A. T. Sapozhnikov
VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 3. P. 9-14.
An equation of state is proposed for graphite and diamond to compute the pressure and specific internal energy from density and temperature. The pressure and energy are thermodynamically consistent. The potential components of pressure and energy are described using Born-Meyer theory. The Gruneisen coefficient depends only on density for diamond and on temperature for graphite. The equation of state describes well the experimental data on shock compressibility, heat capacity, thermal expansion and phase equilibrium. It can be used in computational models and codes for graphite-diamond phase transition under dynamic leads.
|ON STABILITY OF A LOCALLY HEATED ROUND PLATE UNDER COOLING
N. A. Guk, N. B. Makarenko, N. I. Obodan
VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 3. P. 15-19.
The resolution relations are obtained to study the dynamic behavior of round plates under pulse heat impact in terms of geometric and physical nonlinearity in bound geometry. The numerical algorithm is described. The computational results are given for the axisymmetric behavior of plates under heating for various heat spot sizes. Possible loss of stability is considered for structures under rapid cooling.
|ON NUMERICAL SOLUTION OF ELECTRON HYDRODYNAMICS EQUATIONS FOR HIGHLY MAGNETIZED ELECTRONS
V. P. Bashurin, A. I. Golubev, V. S. Shagalieva
VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 3. P. 20-24.
The problem setup is presented for the magnetic field flow in the cavity resulting from the expansion of the ionized cloud into homogeneous magnetized plasma. The problem includes both magnetic field diffusion to plasma due to collisions and plasma turbulence and magnetic field transport by Hollow currents.
The dispersion properties of equations are discussed. The numerical algorithm is given for this problem. The discussion is presented for the restrictions of the timestop occuring if the electrons are highly magnetized from the conditions of difference scheme stability and iteration convergence when solving nonlinear difference equations.
|MATHEMATICAL MODEL FOR POROUS MEDIUM DYNAMICS
A. T. Sapozhnikov, P. D. Gershchuk
VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 3. P. 25-32.
A semi-empirical model is proposed to describe the pressure ш the porous medium under deformation and heating. The model reflects the basic experimental behavior features of porous material under deformation.
The algorithm is given for numerical integration of the energy conservation law for porous medium in terms of viscosity and energy release. 1 lie formulas are proposed for the calculation of the shift modulus, bulk modulus, dynamic strength yield and spalling resistance of the porous medium.
The model is intended for the program implementation of solid and porous medium dynamics. The model capabilities are demonstrated through the description of properties of carbon and some metals. The computational results are given for the impact of a thin plate against porous copper layer.
|STUDYING RAYLEIGH-TAYLORINSTABILITY OF A THIN LIQUID LAYER IN 3D FORMULATION
S. M. Bakhrakh, G. P. Simonov
VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 3. P. 33-38.
The solution is obtained for the perturbation evolution of the accelerated thin plane layer in 3D geometry. The solution dependence on dimensionless parameters is studied. The analitical relations are confirmed by numerical results.
|ANALITICAL AND NUMERICAL STUDY FOR RAYLEIGH TAYLOR INSTABILITY OF A THIN LIQUID LAYER
S. M. Bakhrakh, G. P. Simonov
VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 3. P. 39-46.
Using the equation for a thin liquid layer in Lagrangian form the analytical solutions were obtained for the Rayleigh-Taylor instability problem. The role is clarified for dimensionless parameters determining the shape of initial perturbation.
The analytical relations agree both with numerical solutions in the shell approximation and with those of the full system of hydrodynamic equations.
|ON THE ISSUE OF CARBON EQUATION OF STATE AND PHASE DIAGRAM
V. V. Dremov, S. I. Samarin
VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 3. P. 47-51.
Monte-Carlo calculations of diamond thermodynamic properties have been carried out to check correctness of graphite and diamond semiempirical equations of state (EOS) in the regions of phase diagram where experimental data are absent.
On the basis of these EOSs and Grover’s model of liquid state EOS of liquid carbon have been constructed and carbon phase diagram (graphite and diamond melting curves and triple point) has been calculated. Comparison о calculated and experimental Hugoniots has stated a question about diamond melting curve.
|EULERIAN TECHNIQUE FOR THE CALCULATION OF 3D ELASTIC- PLASTIC FLOWS IN MULTICOMPONENT MEDIUM
A. L. Stadnik, V. I. Tarasov, Yu. V. Yanilkin
VANT. Ser.: Mat. Mod. Fiz. Proc.. 1995. No 3. P. 52-60.
The description is given for the finite-difference scheme in Eulerian variables implemented within TREK complex and intended for 3D calculations of multicomponent medium flows. The classes of problems to be computed demonstrate strong deformations of interfaces. To localize and avoid the computational diffusion of interfaces we use the method of consentrations. The computational results are given for some problems that are compared with 2D results and experimental data.
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