A study of the Hasegawa--Wakatani equations using an implicit explicit backward differentiation formula

Linda Stals

Abstract


The Hasegawa--Wakatani system of equations may be used to predict and study the behaviour of plasma flow. A recent analytical study of the use of linear multistep methods to solve the Hasegawa--Wakatani equations showed the backward differentiation formulas to be the most stable. Because the backward differentiation formulas require a solution of a large dense system of equations, so we implemented an implicit explicit version of the formula. We study the performance of the implicit explicit backward differentiation formula on some example problems where the behaviour of the Hasegawa--Wakatani equation is predictable. These results suggest that the implicit explicit method is appropriate to use with the Hasegawa--Wakatani equations.

References
  • S. J. Camargo, D. Biskamp, and B. D. Scott, Resistive drift-wave turbulence, Phys. Plasmas, 1, 1995, 48--62. http://www.ldeo.columbia.edu/ suzana/papers/camargo_biskamp_scott95.pdf
  • S. J. Camargo, M. K. Tippett, and I. L. Caldas, Nonmodal energetics of resistive drift waves, Phys. Rev. E, 58, 1998, 3693--3704. doi:10.1103/PhysRevE.58.3693
  • G. Dahlquist, On the relation of G-stability to other stability concepts for linear multistep methods, in Topics In Numerical Analysis {III}, J. H. Miller, ed., pages 67--80. Academic Press, London, 1977.
  • G. Dahlquist, G-stability is equivalent to A-stability, BIT, 18, 1978, 384--401. doi:10.1007/BF01932018
  • T. Geveci, On the rate of convergence of the Fourier spectral method for the Navier--Stokes equations, Calcolo, 26, 1989, 185--195. doi:10.1007/BF02575728
  • A. Hasegawa and M. Wakatani, Plasma edge turbulence, Phys. Rev. Lett., 50, 1983, 682--686. doi:10.1103/PhysRevLett.50.682
  • A. T. Hill, Global dissipativity for A-stable methods, SIAM J. Numer. Anal., 34, 1997, 119--142. doi:10.1137/S0036142994270971
  • R. LeVeque, G. Dahlquist, and D. Andree, Computations related to G-stability of linear multistep methods, Tech. Rep. STAN-CS-79-738, Stanford University, Computer Science Department, School of Humanities and Sciences, May 1979. ftp://reports.stanford.edu/pub/cstr/reports/cs/tr/79/738/CS-TR-79-738.pdf
  • R. Numata, R. Ball, and R. L. Dewar, Bifurcation in electrostatic resistive drift wave turbulence, Phys. Plasmas, 14, 102312, 2007, 8 Pages. http://arxiv.org/abs/0708.4317
  • T. S. Pedersen, P. K. Michelsen, and J. J. Rasmussen, Resistive coupling in drift wave turbulence, Plasma Phys. Control. Fusion, 38, 1996, 2143--2154. doi:10.1088/0741-3335/38/12/008
  • L. Stals, R. Numata, and R. Ball, Stability analysis of time stepping for prolonged plasma fluid simulations. Accepted for publication in SIAM Journal of Scientific Computing.

Full Text:

PDF BibTeX


DOI: http://dx.doi.org/10.21914/anziamj.v50i0.1461



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.