Development of a High-order Flux Reconstruction Framework for Solar and Astrophysical Magnetohydrodynamics: Methods and Benchmarks

Abstract High-order flux reconstruction (FR) offers excellent accuracy and efficiency on unstructured meshes, yet its potential remains largely untapped in solar, astrophysical, and space-weather modeling, where production magnetohydrodynamics (MHD) codes predominantly rely on low-order schemes. This reliance limits the resolution of multiscale features and introduces excess numerical dissipation in various MHD regimes. We introduce a high-order FR framework for ideal/resistive MHD with hyperbolic divergence cleaning, purpose-built for astrophysical applications. The formulation is modular and monolithic, and is compatible with both explicit and implicit time integration and curved geometries. It is designed to retain high-order accuracy in smooth regions while remaining practical in the presence of strong gradients. To this end, we incorporate a cell-wise order-blending mechanism that smoothly mixes the standard high-order FR residual with a locally constructed low-order ( P 0) counterpart; the blending is activated by a bounded, neighbor-aware modal-energy indicator, adding robustness without sacrificing the high-order character where the solution is smooth. We benchmark the high-order framework on a wide range of MHD flows on structured and unstructured meshes. The results demonstrate that high-order FR provides superior accuracy per degree of freedom, together with robust performance across canonical problems. As a first step toward operational heliophysics applications, we present a quasi-steady inner-heliospheric solar-wind simulation driven by physics-based coronal boundary conditions and compared against in situ observations, demonstrating the framework’s potential for space-weather modeling.