A high-order finite-difference solver for direct numerical simulations of magnetohydrodynamic turbulence

This paper presents the development and validation of a Magnetohydrodynamics (MHD) module integrated into the Xcompact3d framework, an open-source high-order finite-difference suite of solvers designed to study turbulent flows on supercomputers. Leveraging the Fast Fourier Transform library already implemented in Xcompact3d, alongside sixth-order compact finite-difference schemes and a direct spectral Poisson solver, both the induction and potential-based MHD equations can be efficiently solved at scale on CPU-based supercomputers for fluids with strong and weak magnetic field, respectively. Validation of the MHD solver is conducted against established benchmarks, including Orszag-Tang vortex and MHD channel flows, demonstrating the module's capability to accurately capture complex MHD phenomena, providing a powerful tool for research in both engineering and astrophysics. The scalability of the Xcompact3d framework remains intact with the incorporation of the MHD module, ensuring efficient performance on modern high-performance clusters. This paper also presents new findings on the evolution of the Taylor-Green vortex under an external magnetic field for different flow regimes.本文介绍了集成于Xcompact3d框架的磁流体动力学（Magnetohydrodynamics, MHD）模块的开发与验证工作。Xcompact3d是一款开源的高阶有限差分求解器套件，专为超算环境下的湍流流动研究设计。该模块依托Xcompact3d中已集成的快速傅里叶变换（Fast Fourier Transform）库、六阶紧致有限差分格式以及直接谱泊松求解器，可分别在基于CPU的超算平台上高效规模化求解强磁场流体与弱磁场流体对应的感应式与势函数形式磁流体动力学方程。本MHD求解器通过与经典基准测试案例（包括奥泽格-唐涡旋及MHD槽道流）对比完成验证，结果表明该模块可精准捕捉复杂磁流体动力学现象，为工程与天体物理领域的研究提供了强有力的工具。集成该MHD模块后，Xcompact3d框架的可扩展性得以完整保留，确保在现代高性能计算集群上仍可实现高效运行。此外，本文还针对不同流动工况，给出了外磁场作用下泰勒-格林涡旋（Taylor-Green vortex）演化的全新研究发现。