Abstract
This paper is concerned with the numerical solution of partial differential equations describing fluid flow problems in real space and in phase space. One important goal is to show conclusively that the Accurate Space Derivative methods can be used with success for solving such problems numerically. We describe a method for the numerical solution of the Korteweg-de Vries-Burgers equation. We show numerically that the solution of this equation evolves asymptotically into a steady shock wave with monotonic and oscillatory profile. We present numerical solutions of the Vlasov-Poisson system of equations which describes the motion of an ideal incompressible fluid in phase space. These problems are related to longitudinal oscillations in two- and three-dimensional phase space.
Chapter PDF
Similar content being viewed by others
References
Armstrong, T.P., Harding, R.C., Knorr, G., and Montgomery, D. Methods in Computational Physics, 9, pp. 30–84, Academic Press, New York (1970).
Bekefi, G. Radiation Processes in Plasmas, p. 238, Wiley, New York (1966).
Berk, H.L., and Roberts, K.V. Methods in Computational Physics, 9, pp. 87–134, Academic Press, New York (1970).
Bernstein, I.B. Phys. Rev., 109, p. 10, (1958).
Canosa, J., Gazdag, J., Fromm, J.E., and Armstrong, B.H. Phys. Fluids, 15, p. 2299 (1972).
Canosa, J., and Gazdag, J. Proceedings of the Sixth Conference on Numerical Simulation of Plasmas, Berkeley, California, p. C9, July 16–18, 1973.
Canosa, J., and Gazdag, J. Asymptotic Behavior of Nonlinear Vlasov Plasmas, submitted to Phys. Fluids.
Canosa, J., Gazdag, J., and Fromm, J.E. The Recurrence of the Initial State in the Numerical Solution of the Vlasov Equation, submitted to J. Comp. Phys.
Davidson, R.C. Methods in Nonlinear Plasma Theory, Academic Press (1972), Chapter 4.
Fromm, J.E. IBM J. Res. Dev. 15, p. 186 (1971).
Gazdag, J. Proc. Fourth Conference on Numerical Simulation of Plasmas, Washington, D.C., p. 665, Nov. 2,3, 1970.
Gazdag, J. Numerical Convective Schemes Based on Accurate Space Derivatives, to be published in J. Comp. Phys.
Gazdag, J. Proceedings of the 1973 Summer Computer Simulation Conference, Montreal, pp. 40–45, July 17–19, 1973.
Gazdag, J., and Canosa, J. Numerical Solution of Fisher's Equation, to be published in the J. of Applied Probability.
Gazdag, J., and Canosa, J. Proceedings of the Sixth Conference on Numerical Simulation of Plasmas, Berkeley, California, p. C8, July 16–18, 1973.
Gitomer, S.J. Phys. Fluids 14, p. 2234 (1971).
Grad, H., and Hu, P.N. Phys. Fluids 10, p. 2596 (1967).
Jeffrey, A., and Kakutani, T. SIAM Review 14, p. 582 (1972).
Johnson, R.S. Phys. Fluids 15, p. 1693 (1972).
Johnson, R.S. J. Fluid Mech. 42, p. 49 (1970).
Lewis, H.R. Phys. Fluids 15, p. 103 (1972).
Morse, R.L. Methods in Computational Physics, 9, pp. 213–239, Academic Press, New York (1970).
Orszag, S.A. J. Fluid Mech. 49, p. 75, Part 1 (1971).
Orszag, S.A. Stud. in Appl. Math. 50, p. 293 (1971).
Orszag, S.A. Stud. in Appl. Math. 51, p. 253 (1972).
Richtmeyer, R.D., and Morton, K.W. Difference Methods for Initial-Value Problems, Interscience Publishers, Second Edition (1967).
Sagdeev, R.Z., and Galeev, A.A. Nonlinear Plasma Theory, (Revised and Edited by T.M. O'Neil and D.L. Book), W.A. Benjamin, Inc., Chapter II (1969).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1974 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gazdag, J. (1974). Flow computations with accurate space derivative methods. In: Glowinski, R., Lions, J.L. (eds) Computing Methods in Applied Sciences and Engineering Part 2. Lecture Notes in Computer Science, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-06769-8_3
Download citation
DOI: https://doi.org/10.1007/3-540-06769-8_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-06769-6
Online ISBN: 978-3-540-38380-2
eBook Packages: Springer Book Archive