Spectral methods in numerical plasma simulation

An introduction is given to the use of spectral methods in numerical plasma simulation. As examples of the use of spectral methods, solutions to the two-dimensional Euler equations in both a simple, doubly periodic region, and on an annulus will be shown. In the first case, the solution is expanded in a two-dimensional Fourier series, while a Chebyshev-Fourier expansion is employed in the second case. A new, efficient algorithm for the solution of Poisson's equation on an annulus is introduced. Problems connected to aliasing and to short wavelength noise generated by gradient steepening are discussed.

[1]  James C. McWilliams,et al.  The emergence of isolated coherent vortices in turbulent flow , 1984, Journal of Fluid Mechanics.

[2]  J. Gazdag.  Time-differencing schemes and transform methods , 1976 .

[3]  Dale B. Haidvogel,et al.  The Accurate Solution of Poisson's Equation by Expansion in Chebyshev Polynomials , 1979 .

[4]  F. R. Hansen,et al.  Finite Larmor radius effects to arbitrary order , 1988 .

[5]  Philip S. Marcus,et al.  Numerical simulation of Jupiter's Great Red Spot , 1988, Nature.

[6]  S. Orszag,et al.  Finite-amplitude stability of axisymmetric pipe flow , 1981, Journal of Fluid Mechanics.

[7]  Pseudo-spectral Simulation of a Two-Dimensional Vortex Flow in a Stratified, Incompressible Fluid , 1981 .

[8]  G. S. Patterson,et al.  Spectral Calculations of Isotropic Turbulence: Efficient Removal of Aliasing Interactions , 1971 .

[9]  Claude Basdevant,et al.  Vorticity and passive-scalar dynamics in two-dimensional turbulence , 1987, Journal of Fluid Mechanics.

[10]  T. A. Zang,et al.  Spectral methods for fluid dynamics , 1987 .

[11]  T. Taylor,et al.  Computational methods for fluid flow , 1982 .

[12]  H. Schamel,et al.  The application of the spectral method to nonlinear wave propagation , 1976 .

[13]  A. Chorin.  Flame advection and propagation algorithms , 1980 .

[14]  S. Orszag.  Accurate solution of the Orr–Sommerfeld stability equation , 1971, Journal of Fluid Mechanics.

[15]  S. Orszag.  Numerical Simulation of Incompressible Flows Within Simple Boundaries. I. Galerkin (Spectral) Representations , 1971 .

[16]  Y. Salu,et al.  Use of the spectral method for two- and three-dimensional guiding center plasmas , 1975 .

[17]  John V. Shebalin,et al.  Anisotropy in MHD turbulence due to a mean magnetic field , 1983, Journal of Plasma Physics.

[18]  D. Gottlieb,et al.  Numerical analysis of spectral methods , 1977 .