This project will extend the high-order CFD solver Neko (neko.cfd) to compressible magnetohydrodynamics (MHD). Neko is a portable, GPU-ready spectral-element framework written in modern Fortran, designed for large-scale turbulence on heterogeneous supercomputers. I am a main developer of Neko. The work targets efficient, accurate, and robust MHD at scale. We will bring recent high-order MHD advances into Neko’s spectral-element stack. My prior work established entropy-compatible viscous regularization for ideal MHD that preserves positivity and the minimum-entropy principle. I also developed residual-based and nodal artificial viscosity for sharp, high-order shock capturing, and a structure-preserving scheme that maintains invariant domains and exact magnetic involutions. These results guide the design here: 1. Dao, T. A., Nazarov, M., & Tomas, I. (2024). A structure preserving numerical method for the ideal compressible MHD system. Journal of Computational Physics, 508, 113009. 2. Dao, T. A., & Nazarov, M. (2024). A nodal based high order nonlinear stabilization for finite element approximation of Magnetohydrodynamics. Journal of Computational Physics, 512, 113146. 3. Dao, T. A., & Nazarov, M. (2022). Monolithic parabolic regularization of the MHD equations and entropy principles. Computer Methods in Applied Mechanics and Engineering, 398, 115269. 4. Dao, T. A., & Nazarov, M. (2022). A high-order residual-based viscosity finite element method for the ideal MHD equations. Journal of Scientific Computing, 92(3), 77. Concretely, we will (i) implement an entropy-residual shock sensor and nodal artificial viscosity adapted to spectral elements, (ii) add a structure-preserving operator split that couples a compressible Euler core with magnetic source terms, and (iii) enforce divergence control compatible with Neko’s SEM basis and mesh operations. Together these yield high-order accuracy in smooth regions and stability near shocks, while keeping strict time-step controls and conservation properties. Neko already runs efficiently on CPU and GPU clusters (CUDA/HIP) through a device-abstraction layer. We will reuse these backends for MHD kernels (e.g., fluxes, Riemann-free stabilization, curl operations) and maintain single-source Fortran. This ensures portability across systems like Dardel, LUMI, and Frontier, and supports strong/weak scaling studies without code forks. We will validate the new module on standard 2D/3D tests (Brio–Wu, Orszag–Tang, rotor, blast) and on large-eddy/implicit LES targets relevant to fusion and space physics. Metrics include accuracy order, shock resolution, divergence error, invariant-domain compliance, and node-hour efficiency. The outcome will be: (1) an open MHD extension in Neko, (2) reproducible scaling benchmarks on modern GPU systems, and (3) method papers and an integration guide for users. By combining proven MHD theory with Neko’s HPC strengths, this project delivers a production-quality, performance-portable MHD capability for the community.