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A Two-Dimensional Operator-Difference Scheme for Fluid Dynamics in Lagrangean Coordinates on an Irregular Triangular Grid with the Property of Local Approximation near the Symmetry Axis

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Abstract

The projection approach is applied to construct and investigate an operator-difference scheme for fluid dynamics in Lagrangean variables which has first-order local approximation in the axisymmetric case near the symmetry axis. The scheme also has operator properties that make it suitable for rederiving and substantiating previous results, methods, and algorithms.

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REFERENCES

  1. A. A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  2. A. A. Samarskii, V. F. Tishkin, A. P. Favorskii, and M. Yu. Shashkov, “Operator difference schemes,” Diff. Uravn., 17, No. 7, 1317-1327 (1981).

    Google Scholar 

  3. Yu. P. Popov, Difference Methods in Fluid Dynamics [in Russian], Nauka, Moscow (1992).

    Google Scholar 

  4. A. A. Samarskii, A. V. Koldoba, Yu. A. Poveshchenko, V. F. Tishkin, and A. P. Favorskii, Difference Schemes on Irregular Networks [in Russian], Kriterii, Minsk (1996).

    Google Scholar 

  5. M. P. Galanin and Yu. P. Popov, Quasi-Stationary Electromagnetic Fields in Nonhomogeneous Media. Mathematical Modeling [in Russian], Nauka-Fizmatlit, Moscow (1995).

    Google Scholar 

  6. N. V. Mikhailova, V. F. Tishkin, N. N. Tyurina, A. A. Favorskii, and M. Yu. Shashkov, “Numerical simulation of two-dimensional fluid flows on a variable structure grid,” Zh. Vychisl. Matem. Mat. Fiziki, 26, No. 9, 1392-1406 (1986).

    Google Scholar 

  7. B. M. Chetverushkin, Mathematical Modeling of the Dynamics of Radiating Gases [in Russian], Nauka, Moscow (1985).

    Google Scholar 

  8. V. M. Goloviznin, A. A. Samarskii, and A. P. Favorskii, “Variational approach to the construction of finite-difference models in hydrodynamics,” Dokl. Akad. Nauk SSSR, 235, No. 6, 1285-1288 (1977).

    Google Scholar 

  9. N. V. Ardelyan, K. V. Kosmachevskii, and S. V. Chernigovskii, Topics of Construction and Analysis of Completely Conservative Difference Schemes in Magnetohydrodynamics [in Russian], Izd. MGU, Moscow (1987).

    Google Scholar 

  10. N. V. Ardelyan and I. S. Gushchin, “An approach to the construction of completely conservative difference schemes,” Vestnik MGU, Comput. Math. Cybern., No. 3, 3-10 (1982).

  11. N. V. Ardelyan and K. V. Kosmachevskii, “An implicit free-Lagrange method for computing two-dimensional magnetohydrodynamic flows,” in: Mathematical Modeling [in Russian], Izd. MGU, Moscow (1993), pp. 25-44.

    Google Scholar 

  12. A. A. Samarskii and A. V. Gulin, Stability of Difference Schemes [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  13. A. A. Samarskii and E. S. Nikolaev, Methods for Solving of Grid Equations [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  14. J. Ortega and W. Rheinboldt, Iterative Methods for Solving Nonlinear Systems of Equations in Many Unknowns [Russian translation], Mir, Moscow (1975).

    Google Scholar 

  15. N. V. Ardelyan, “Convergence of difference schemes for two-dimensional equations of acoustics and Maxwell equations,” Zh. Vychisl. Matem. Mat. Fiziki, 23, No. 5, 1168-1176 (1983).

    Google Scholar 

  16. N. V. Ardelyan, “Using iterative method for the implementation of implicit difference schemes in two-dimensional magnetohydrodynamics,” Zh. Vychisl. Matem. Mat. Fiziki, 23, No. 6, 1417-1426 (1983).

    Google Scholar 

  17. V. A. Gasilov, V. Kh. Kurtmulaev, V. M. Goloviznin, et al., “Simulation of toroidal plasma compression by a quasi-spherical liner,” Preprint IPM AN SSSR No. 71, Moscow (1979).

  18. A. V. Solov'ev, E. V. Solov'eva, and V. F. Tishkin, “Computing time-dependent two-dimensional fluid-dynamic problems by the Dirichlet particle method,” Preprint IPM AN SSSR No. 97, Moscow (1987).

  19. N. N. Anuchina, K. I. Babenko, S. K. Godunov, et al., Theoretical Principles and Design of Numerical Algorithms for Problems of Mathematical Physics [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  20. Advances in the Free-Lagrange Method, Springer, Berlin (1991).

  21. V. M. Goloviznin, V. K. Korshunov, and A. A. Samarskii, “Two-dimensional difference schemes of magnetohydrodynamics on triangular Lagrange grids,” Zh. Vychisl. Matem. Mat. Fiziki, 22, No. 4, 926-942 (1982).

    Google Scholar 

  22. A. Ya. Boiko, “Construction of completely conservative difference schemes using projection algorithms,” Zh. Vychisl. Matem. Mat. Fiziki, 22, No. 4, 544-556 (1987).

    Google Scholar 

  23. N. V. Ardelyan, K. V. Kosmachevskii, and S. V. Chernigovskii, “Some features of the computation of two-dimensional fluid dynamic problems on irregular triangular grids,” in: Computational Mathematics and Computer Software [in Russian], Izd. MGU, Moscow (1985), pp. 10-20.

    Google Scholar 

  24. N. V. Ardeljan, G. S. Bisnovatyi-Kogan, K. V. Kosmachevskii, and S. G. Moiseenko, “An implicit Lagrangean code for the treatment of nonstationary problems in rotating astrophysical bodies,” Astron. Astrophys. Suppl. Ser., 115, 573-594 (1996).

    Google Scholar 

  25. N. V. Ardeljan, G. S. Bisnovatyi-Kogan, and S. G. Moiseenko, “Nonstationary magnetorotational processes in a rotating magnetized cloud,” Astron. Astrophys., 355, 1181-1190 (2000).

    Google Scholar 

  26. N. V. Ardelyan, V. L. Bytchkov, K. V. Kosmachevskii, S. N. Chuvashev, N. D. Malmuth, “Modeling of plasmas in electron beams and plasma jets for aerodynamic applications,” in: Proceedings of the 32nd AIAA Plasma Dynamics and Lasers Conference and 4th Weakly Ionized Gases Workshop (June 11-14, 2000, Anaheim, CA), American Institute of Aeronautics and Astronautics (2001).

  27. N. V. Ardelyan, A. S. Kamrukov, N. P. Kozlov, K. V. Kosmachevskii, Yu. P. Popov, Yu. S. Protasov, A. A. Samarskii, and S. N. Chuvashev, “Simulation of radiating plasma-dynamic discharges of an erosion-type magnetoplasma compressor,” Dokl. Akad.Nauk SSSR, 292, No. 3, 590-593 (1987).

    Google Scholar 

  28. N. V. Ardelyan, A. S. Kamrukov, N. P. Kozlov, K. V. Kosmachevskii, Yu. P. Popov, Yu. S. Protasov, A. A. Samarskii, and S. N. Chuvashev, “Magneto-fluid-dynamic effects in the interaction of gas with erosion plasma streams in a magnetoplasma compressor,” Dokl. Akad. Nauk SSSR, 292, No. 1, 78-81 (1987).

    Google Scholar 

  29. L. A. Oganesyan and L. A. Rukhovets, Variational-Difference Methods for Solving Elliptical Equations [in Russian], Izd. AN Arm. SSR, Erevan (1979).

    Google Scholar 

  30. N. V. Ardelyan, “A method for investigating the convergence of nonlinear difference schemes,” Diff. Uravn., 23, No. 7, 1116-1127 (1987).

    Google Scholar 

  31. N. V. Ardelyan, “Solvability and convergence of nonlinear difference schemes,” Dokl. Akad. Nauk SSSR, 302, No. 6,1289-1292 (1988).

    Google Scholar 

  32. N. V. Ardeljan and K. V. Kosmachevskii, “An implicit free Lagrange method with finite element operators for the solution of MHD problems,” in: Finite Elements in Fluids, New Trends and Applications, IACM Special Int. Conf., Venice, Italy, Oct. 15-21, 1995, Part 2 (1995), pp. 1099-1108.

  33. N. V. Ardelyan, K. V. Kosmachevskii, N. P. Kozlov, Yu. P. Popov, Yu. S. Protasov, A. A. Samarskii, and S. N. Chuvashev, “Simulation and theoretical analysis of radiating plasma-dynamic discharges,” in: Radiation Plasma Dynamics [in Russian], Part 1, Energoizdat, Moscow (1991), pp. 191-250.

    Google Scholar 

  34. N. V. Ardeljan, “Iterative methods for solving of implicit difference schemes of MHD,” A. Angew. Math. Mech., Berlin, Supplement I, ICIAM/GAMM95, Numerical Analysis, Scientific Computing, Computer Science, 76, 123-126 (1996).

    Google Scholar 

  35. N. V. Ardelyan and M. N. Sablin, “An iterative method for the system of operator equations arising in the solution of implicit difference schemes in fluid dynamics,” Vestnik MGU, Ser. 15, Comput. Math. Cybern., No. 4, 7-12 (1993).

  36. N. V. Ardelyan and Yu. P. Popov, “Specific features of the application of numerical methods in the problem of magnetorotational supernova explosion,” Preprint IPM AN SSSR No. 107(1979).

  37. N. V. Ardelyan, “Application of Newton's method for the implementation of difference schemes in fluid dynamics,” in: Computational Methods and Programming [in Russian], Izd. MGU, Moscow, 35, 136-144 (1981).

    Google Scholar 

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Authors
  1. M. N. Sablin
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  2. N. V. Ardelyan
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Sablin, M.N., Ardelyan, N.V. A Two-Dimensional Operator-Difference Scheme for Fluid Dynamics in Lagrangean Coordinates on an Irregular Triangular Grid with the Property of Local Approximation near the Symmetry Axis. Computational Mathematics and Modeling 14, 93–107 (2003). https://doi.org/10.1023/A:1022999221825

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