A Full-Induction Magnetohydrodynamics Solver for Liquid Metal Fusion Blankets in Vertex-CFD

TL;DR

This work addresses the need for a full-induction MHD description in liquid metal fusion blankets, where transient magnetic fields during disruptions invalidate inductionless approximations. The authors develop a full-induction AC-GLM-MHD solver in the open-source Vertex-CFD framework, employing finite-element discretization, implicit SDIRK time integration, and inexact Newton solves, with divergence-control via GLM and Godunov–Powell terms and HPC portability through Trilinos and Kokkos. They verify the method against standard benchmarks (magnetic advection-diffusion, circularly polarized Alfvén waves, divergence-cleaning tests, current sheets, lid-driven cavities) and apply it to an idealized blanket model in 2.5D and 3D, demonstrating accurate wave propagation, Hartmann-layer resolution, and good agreement with recent quasi-2D simulations. The study establishes a computational foundation for transient MHD simulations in liquid metal blankets and points to future extensions including multi-material coupling, plasma interactions, and solver performance optimizations.

Abstract

Multiphysics modeling of liquid metal fusion blankets, which produce tritium and convert energy of neutrons created via fusion reactions into heat, is crucial for predicting performance, ensuring structural integrity, and optimizing energy production. While traditional blanket modeling of liquid metal flows during normal steady operating conditions commonly employs the inductionless approximation of the magnetohydrodynamics (MHD) equations, transient scenarios, when the plasma-confining magnetic field varies on millisecond time scales, require a full-induction MHD approach that dynamically evolves the magnetic field via the time-dependent induction equation. This paper presents the formulation, implementation, and initial verification of a full-induction MHD solver integrated within the open-source Vertex-CFD framework, which aims to achieve tight multiphysics coupling, a flexible software design enabling easy extension and addition of physics models, and performance portability across computing platforms. The solver utilizes finite element spatial discretization, implicit Runge--Kutta time integration, and an inexact Newton method to solve the resulting discrete nonlinear system, leveraging Trilinos packages for efficient computation. Verification against selected benchmark problems demonstrates accuracy and robustness of the solver. Furthermore, when the solver is applied to an idealized blanket model in 2.5D and full 3D, results obtained with Vertex-CFD are in good agreement with recently published quasi-2D simulations. These findings establish a computational foundation for future simulations of transient MHD phenomena in liquid metal blankets with Vertex-CFD, and open avenues for future extensions and performance optimizations.

Figures (21)

• Figure 1: Divergence cleaning test: $\nabla\cdot\boldsymbol{B}$ at several times under the effects of various cleaning terms: only GP sources, (first row; GP); only GLM divergence cleaning without damping, $c_{h}=50$ and $\alpha=0$ (second row; GLM No Damp); only GLM divergence cleaning, $c_{h}=50$ and $\alpha=c_h/0.18$ (third row; GLM Damp); GP sources and GLM divergence cleaning without damping, $c_{h}=50$ and $\alpha=0$ (fourth row; GP+GLM ND); and GP sources and GLM divergence cleaning, $c_{h}=50$ and $\alpha=c_h/0.18$ (fifth row; GP+GLM D).
• Figure 2: Impact of divergence cleaning parameters on the time evolution of maximum local divergence metrics.
• Figure 3: Comparison of the Vertex-CFD solution against the exact solution for the current sheet problem obtained with a quadrilateral (left) and triangle (right) mesh composed of 50 elements in each Cartesian direction. Fewer markers than nodal points are plotted to reduce marker density.
• Figure 4: Velocity magnitude with streamlines overlaid for the MHD LDC with horizontal initial magnetic field of varying strength.
• Figure 5: Magnetic field magnitude with field lines overlaid for the MHD LDC with horizontal initial magnetic field of varying strength.