Sherwood 2015

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approvedposter_ap_v1.pdf2015-04-03 07:23:13Maurizio Ottaviani
approvedsherwood_2015_ap-1.pdf2015-03-11 02:52:58Maurizio Ottaviani

Applications of asymptotic-preserving (AP) methods to plasma dynamics simulations at realistic dimensionless parameters

Author: Maurizio A. Ottaviani
Requested Type: Poster Only
Submitted: 2015-01-14 02:16:14

Co-authors: F. Deluzet, J. Narski, C. Negulescu and S. Possanner

Contact Info:
bat 513, CEA Cadarache
ST Paul lez Durance, BdR   13108

Abstract Text:
The numerical treatment of singularly perturbed problems has advanced significantly with the advent of asymptotic-preserving (AP) techniques [1]. AP schemes are designed to work accurately in both the limit when a small parameter is of order unity and when it approaches zero.

In this work, we present two applications of AP methods to the context of plasma physics.

The first one concerns the strongly anisotropic transport of a scalar in magnetic island geometry. Here the small parameter is the ratio of the perpendicular to the parallel transport coefficient. A suitable AP method is constructed which works on a uniform grid, with both open and closed field lines, without requiring alignment of the grid to the magnetic field. The strength of the method is demonstrated for values of the small parameter as low as 10^{-10} [2].

The second application is to resistive MHD (RMHD) in two dimensions. Numerical simulations of RMHD are notoriously challenging because of the disparate time-scales, Alfven and resistive, and because of the formation of thin internal layers, especially in the nonlinear phase. Upon suitable rescaling of the original equations, the small parameter turns out to be the inverse of the square of the Lundquist number. The tearing mode evolution and the formation of a magnetic island are considered as a test case. One finds that the scheme is able to reproduce efficiently the three regimes of the island dynamics, linear, Rutherford growth and saturation, with good agreement with known analytical results [3] for this problem. The scheme is shown to work well at S=10^8, with the quality of the simulation depending essentially on the resolution necessary to treat the small visco-resistive layer occurring around the separatrix [4].

[1] S. Jin, SIAM J. Sci. Comput. 21, 441 (1999). [2] J. Narski and M. Ottaviani , CPC 185, 3189 (2014).[3] D. F. Escande and M. Ottaviani, PLA, 323, 278 (2004). [4] F.Deluzet et al., JCP 280, 602 (2015).


March 16-18, 2015
The Courant Institute, New York University