Scalable and Accurate Simulation of Magnetized Plasmas

Project Overview

The overarching goal of this project was to explore finite-element approaches for simulating magnetized plasmas with unprecedented accuracy that scale well to next-generation high-performance-computing platforms. Magnetic confinement fusion energy may one day provide a safe, sustainable energy source for the foreseeable future. However, the physics of magnetized plasmas is strongly anisotropic with respect to the direction of the magnetic field lines and this leads to numerical issues that are difficult to address. We developed a software framework where new methods can be tested and applied and where performance can be quantitatively measured through an extensive suite of test problems. We demonstrated the ability of adaptive mesh refinement and scalable preconditioning methods to provide a significant reduction in computational work required to solve for the anisotropic equilibrium of magnetized edge plasmas. We found highly accurate finite-element exterior calculus formulations of two-dimensional magnetized plasma models that conserve quadratic invariants such as energy and enstrophy. In fact, we discovered that the best accuracy was obtained using a discontinuous Galerkin approach that exactly conserves energy while dissipating enstrophy. These are significant advances over the state of the art in the field of finite-element plasma modeling.

Mission Impact

This project developed finite-element methods and simulation tools for magnetized plasmas that surpass the state of the art in the field. These accomplishments ensure LLNL's role as a leader in fusion-plasma simulation and in developing advanced numerical methods and software tools. The project also allowed two promising postdoctoral researchers to be converted to staff. Hence, the goals of this project were closely aligned with LLNL's core competencies in high-energy-density science (HEDS) and high-performance computing. The new methods led to more efficient and accurate plasma models that will help to enable the development of safe, sustainable nuclear-fusion energy. These same methods can be used in other HEDS application areas, including magnetized target inertial confinement fusion, space physics, and astrophysics. Thus, this project helped to develop the science and technology tools and capabilities that NNSA and DOE need to meet future national-security challenges.

Publications, Presentations, and Patents

Campos, A. et al. "Finite-Element Exterior-Calculus Simulations of Extended Hasegawa-Wakatani Drift-Wave Turbulence." Poster, International Sherwood Fusion Theory Workshop, Santa Rosa, CA. April 2022. LLNL-POST-833281.

Campos, A. et al. "High-Order Finite-Element Simulations of Forced Dissipative Hasegawa-Mima Turbulence." Presentation, 63rd Annual Meeting of the APS Division of Plasma Physics, Pittsburgh, PA. November 2021. LLNL-PRES-828733.

Dimits, A. M. et al. "Finite-Element Solution of a Vorticity Transport Model Including RF Antenna Effects and Application to Scrape-Off-Layer-Turbulence Simulations." International Sherwood Fusion Theory Workshop, Virtual. August 2021. LLNL-PRES-825760.

Dimits, A. M. et al. "Finite-Element Solution of a Vorticity Transport Model Including RF Antenna Effects and Application to Scrape-Off-Layer Turbulence Simulations." Transport Task Force Workshop, Virtual. April 2021. LLNL-PRES-821633.

Dimits, A. M. et al. "Finite-Element Solution of a Vorticity Transport Model Including RF Antenna Effects and Application to Scrape-Off-Layer-Turbulence Simulations." 62nd Annual Meeting of the APS Division of Plasma Physics, Virtual. November 2020; bibcode 2020APS..DPPB11007D.

Holec, M., et al. "Curved Mesh and Adaptive Mesh Refinement Strategies for Strong Magnetic Anisotropy." Poster, 64th Annual Meeting of the APS Division of Plasma Physics, Spokane, WA. October 2022. LLNL-POST-821594.

Holec, M. et al. "Energy and Enstrophy Conserving High-Order Temporal-Spatial Method for Drift -Reduced MHD." International Sherwood Fusion Theory Workshop, Santa Rosa, CA. April 2022. LLNL-PRES-833448.

Holec, M. et al. "Advanced Energy and Enstrophy Conserving FEM for Drift-Reduced MHD." 63rd Annual Meeting of the APS Division of Plasma Physics, Pittsburgh, PA. November 2021. LLNL-PRES-828745.

Holec, M. et al. "Energy and Enstrophy Conserving Modeling of Drift -Reduced MHD Using High-Order Time-Space Finite Element Methods." International Sherwood Fusion Theory Workshop. Virtual. August 2021. LLNL-PRES-825833.

Holec, M. et al. "Energy and Enstrophy Conserving Modeling of Drift -Reduced MHD Using High-Order Time-Space Finite Element Methods." Transport Task Force Workshop, Virtual. April 2021. LLNL-POST-821597.

Holec, M. et al. "MFEM For Magnetized Edge Plasma: Finite Element Spaces and Block Preconditioning Strategies." SIAM Conference on Computational Science and Engineering (CSE21), Virtual. March 2021. LLNL-POST-819386.

Holec, M. et al. "High-Order Finite Element Framework for Drift-Reduced MHD." 62nd Annual Meeting of the APS Division of Plasma Physics, Virtual. November 2020. LLNL-PRES-816528.

Joseph, I. et al. "Finite Element Simulation of Magnetized Edge Plasma Turbulence." 63rd Annual Meeting of the APS Division of Plasma Physics, Pittsburgh, PA. November 2021. LLNL-PRES-828634.

Joseph, I. et al. "Energy and Enstrophy Conserving Finite Element Methods for Plasma Turbulence." Transport Task Force Workshop, Santa Rosa, CA. April 2022. LLNL-PRES-833450.

Joseph, I. et al. "High-Order Finite Element Simulation of Magnetized Edge Plasma Turbulence." Transport Task Force Workshop, Virtual. April 2021. LLNL-PRES-821560.

Joseph, I. et al. "Magnetized Edge Plasma Fluid Simulation Using High-Order Finite Elements." 63rd Annual Meeting of the APS Division of Plasma Physics, 62nd Annual Meeting of the APS Division of Plasma Physics. Virtual. November 2020. LLNL-PRES-816362.

Southworth, B. S. et al. "Fast, Parallel, High-Order Simulation of the Extended Magnetohydrodynamics Model." 62nd Annual Meeting of the APS Division of Plasma Physics, Virtual. November 2020. LLNL-PRES-816664.

Vogl, C. J. et al. "MFEM for Magnetized Edge Plasma: Tackling Anisotropy with Curved and Adaptive Meshes." International Sherwood Fusion Theory Workshop, Virtual. August 2021. LLNL-PRES-825759.

Vogl, C. J. et al. "MFEM for Magnetized Edge Plasma: Tackling Anisotropy with Curved and Adaptive Meshes." Transport Task Force Workshop, Virtual. April 2021. LLNL-POST-821594.

Vogl, C. J. et al. "MFEM for Magnetized Edge Plasma: Tackling Anisotropy with Curved and Adaptive Meshes." SIAM Conference on Computational Science and Engineering (CSE21), Virtual. March 2021. LLNL-POST-819399.

Zhu, B. et al. "Development of Edge Plasma Turbulence Model Based on MFEM High-Order Finite Element Lbrary." International Sherwood Fusion Theory Workshop, Virtual. August 2021. LLNL-PRES-825669.