Abstract Details
Abstracts
Author: Golo A. Wimmer
Requested Type: Consider for Invited
Submitted: 2026-03-01 20:32:04
Co-authors: K. Lipnikov, B.S. Southworth, X.-Z. Tang
Contact Info:
Los Alamos National Laboratory
P.O. Box 1663
Los Alamos, New Mexico 87545
USA
Abstract Text:
Accurate large-scale simulation of strongly magnetized plasmas in realistic fusion geometries remains a major computational challenge. Fully implicit 3D resistive MHD models with fusion-relevant parameters require robust solvers for stiff magnetic wave coupling and strongly anisotropic heat flux. Existing approaches rely on direct solvers, simplified reactor geometries, or preconditioning strategies that degrade in strongly magnetized regimes, limiting scalability and predictive capability.
We present an efficient, structure-preserving framework for resistive MHD based on compatible finite element spaces. The method preserves the discrete magnetic divergence constraint and energy structure in space, while enabling flexible meshing of realistic tokamak domains. To address stiffness, we employ an implicit-implicit (IMIM) split time discretization that separates fast magnetic waves and anisotropic heat flux from slower sound wave dynamics while retaining full coupling.
The split formulation exposes the magnetic wave operator as an anisotropic curl-curl problem, enabling the use of specialized auxiliary-space Maxwell (AMS) multigrid solvers. At the discrete level, this curl-curl structure is preserved when using a velocity space tailored to the Lorentz-force term, allowing for scalable performance without resorting to direct solvers or prohibitively expensive standard multigrid strategies.
We demonstrate robustness and efficiency of the solver, and accuracy of the structure-preserving discretization, on nonlinear 3D tokamak test cases approaching O(10^7) degrees of freedom, with time steps corresponding to magnetic CFL numbers up to O(10^3) and realistic anisotropic transport coefficients. The approach provides a scalable path toward high-fidelity resistive MHD simulations in general fusion geometries and establishes a foundation for future extended MHD models.
Characterization: 4.0
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