Theoretical and numerical study on discontinuous Galerkin flux reconstruction method in thermal-hydraulic analysis

Nuclear energy is one of the core pillars for global energy transition and carbon neutrality. Nuclear reactor thermal–hydraulic numerical simulation, a key technology for ensuring reactor safety and economy, relies on the discrete solution of convection–diffusion PDEs. As a widely used traditional high-order numerical method, the Local Discontinuous Galerkin (LDG) method has a critical limitation: it requires intermediate auxiliary variables to treat diffusion terms, which substantially increases computational complexity and memory consumption. To overcome this bottleneck, this study proposes a Discontinuous Galerkin-Flux Reconstruction (DG-FR) method and systematically investigates its properties and advantages through theoretical analysis and numerical experiments. The method effectively remedies the drawbacks of LDG and simplifies the discretization of diffusion terms. Theoretical verification confirms that DG-FR possesses strict L2 stability with alternating fluxes. Numerical results demonstrate its overwhelmingly superior computational efficiency over LDG: an average speedup of 35.957% in transient cases, with the advantage growing more evident under mesh refinement and higher polynomial degrees; for steady-state cases, the average speedups reach 11.748% in Runtime and 32.004% in Kernel Time, respectively. In addition, DG-FR shows excellent compatibility with Dirichlet boundary conditions in the asymptotic error behavior of transient problems, making it suitable for long-term engineering simulations with strict physical boundary constraints. The DG-FR method provides an efficient, high-precision numerical solution for nuclear reactor thermal–hydraulic analysis and strongly promotes the engineering application of high-order schemes.