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CONSTRUCTING THE DIFFERENCE SCHEMES FOR THE CALCULATION OF MULTIDIMENSIONAL-TIME-DEPENDENT ELASTIC-PLASTIC FLOWS BASED ON INTERCONVERSION LAW FOR KINETIC AND INTERNAL ENERGY

V.I. Delov, O.V. Senilova, I.D. Sofronov
VANT. Ser.: Mat. Mod. Fiz. Proc 1997. Вып.1. С. 47-48.

      The report proposed an approach to the construction of conservative differential-difference representations of equations describing nonstationary elastic-plastic flows in Lagrangian variables. The method is the further development of 2-D method for the generation of spatial approximations to the equations of motion in gas dynamics [1,2] for elastic-plastic media.
      In this work the matrix of kinetic energy determining the approximation technique for the pressure gradient is taken in the canonical form that is traditionally used in gas-dynamic codes.
      The report presented the difference formulas for the components of deformation rate tensor and the resulting difference approximations for the evaluation of derivatives with respect to the components of the stress deviator.
      The computational results were reported obtained with difference schemes where the grid distribution of quantities in time is taken like in “D” code [3] and the time derivative is approximated with the second order accuracy. The problem describing the elastic oscillations of membrane is taken to show unquestionable advantages of the resulting difference schemes as compared to the classical Wilkins scheme.
      1. Isaev V.N., Sofronov I.D. Construction of discrete models for gas-dynamic equations based on the interconversion law of kinetic and internal energies of continuum // Voprosy Atomnoy Nauki i Tekhniki. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. N 1(15). P. 3-7.
      2. Delov V.I., Isaev V.N., Sofronov I.D. Conservative and invariant differential-difference representations of gas- dynamic equations in cixisymmetric case // Ibid. 1987. N 1. P. 3-10.
      3. Dmitriev N.A., Dmitrieva L.V., Malinovskaya E.V., Sofronov I.D. A method for the calculation of 2-D gas-dynamic problems in Lagrangian variables // Theoretical Fundamentals and Construction of Numerical Algorithms in Computational Physics / Ed. by Babenko K.I. M.: Nauka, 1979. P. 175-200.










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