2007/07/31 by Nuno Loureiro, N. F. Loureiro, G. W. Hammett · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Electromagnetic Simulation and Numerical Methods #Magnetic confinement fusion research #Numerical methods for differential equations #physics.comp-ph #physics.plasm-ph
paper · pdf · doi:10.1016/j.jcp.2008.01.015
published as J. Comp. Phys. 227, 4518 (2008) · Submitted to the Journal of Computational Physics. Clarifications and caveats in response to referees, numerical demonstration of convergence rate, generalized symplectic proof
arxiv created 2008/01/07 · openalex publication_date 2008/01/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An efficient, iterative semi-implicit (SI) numerical method for the time integration of stiff wave systems is presented. Physics-based assumptions are used to derive a convergent iterative formulation of the SI scheme which enables the monitoring and control of the error introduced by the SI operator. This iteration essentially turns a semi-implicit method into a fully implicit method. Accuracy, rather than stability, determines the timestep. The scheme is second-order accurate and shown to be equivalent to a simple preconditioning method. We show how the diffusion operators can be handled so as to yield the property of robust damping, i.e., dissipating the solution at all values of the parameter \mathcal D\dt, where \mathcal D is a diffusion operator and \dt the timestep. The overall scheme remains second-order accurate even if the advection and diffusion operators do not commute. In the limit of no physical dissipation, and for a linear test wave problem, the method is shown to be symplectic. The method is tested on the problem of Kinetic Alfvén wave mediated magnetic reconnection. A Fourier (pseudo-spectral) representation is used. A 2-field gyrofluid model is used and an efficacious k-space SI operator for this problem is demonstrated. CPU speed-up factors over a CFL-limited explicit algorithm ranging from ∼20 to several hundreds are obtained, while accurately capturing the results of an explicit integration. Possible extension of these results to a real-space (grid) discretization is discussed.