Abstract Details
Abstracts
Author: Qi Tang
Requested Type: Poster
Submitted: 2019-02-22 15:56:40
Co-authors: Luis Chacon, John Shadid, Xian-Zhu Tang
Contact Info:
Los Alamos National Laboratory
Los Alamos National Laboratory
Los Alamos, 87545
USA
Abstract Text:
Extended magnetohydrodynamic (XMHD) equations are advanced continuum models to understand the evolution of complex plasma dynamics in large-scale tokamak disruptions. However, solving XMHD numerically is challenging due to its disparity of time scales and nature of nonlinear coupling. Therefore, scalable implicit algorithms based on efficient preconditioning strategies are demanded for XMHD.
In this work, we present several finite elements schemes for a simple model, the reduced resistive MHD equations in 2D. Both explicit and implicit schemes are developed under a scalable C++ framework of MFEM [1]. For the implicit scheme, the physical-based preconditioner for finite difference schemes in [2] will be extended to the finite element framework. In particular, the preconditioner in [2] is generalized to a preconditioner based on Schur complement for the finite element discretization, and the preconditioner effectively removes stiff waves in the system. A Jacobian-free Newton–Krylov method is applied to the resulting nonlinear system. Finally, some benchmark problems will be presented to demonstrate the accuracy and scalability of the implicit scheme. Some comparisons between explicit and implicit schemes will also be shown. This work was supported by DOE OFES.
Acknowledgement. We thank Tzanio Kolev and the MFEM team for the help in this work.
[1] MFEM: Modular Finite Element Methods Library (https://mfem.org).
[2] L. Chacón, D.A. Knoll, J. Finn, An implicit, nonlinear reduced resistive MHD solver, J. Comput. Phys. 178 (1) (2002) 15–36.
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