An Efficient GPU-Accelerated High-Order Upwind Rotated Lattice Boltzmann Flux Solver for Simulating Three-Dimensional Compressible Flows with Strong Shock Waves

This paper presents an efficient and high-order WENO-based Upwind Rotated Lattice Boltzmann Flux Solver (WENO-URLBFS) on graphics processing units (GPUs) for simulating three-dimensional (3D) compressible flow problems. The proposed approach extends the baseline Rotated Lattice Boltzmann Flux Solver (RLBFS) by redefining the interface tangential velocity based on the theoretical solution of the Euler equations. This improvement, combined with a weighted decomposition of the numerical fluxes in two mutually perpendicular directions, effectively reduces numerical dissipation and enhances solution stability. To achieve high-order accuracy, the WENO interpolation is applied in the characteristic space to reconstruct physical quantities on both sides of the interface. The density perturbation test is employed to assess the accuracy of the scheme, which demonstrates 5th- and 7th-order convergence as expected. In addition, this test case is also employed to confirm the consistency between the CPU serial and GPU parallel implementations of the WENO-URLBFS scheme and to assess the acceleration performance across different grid resolutions, yielding a maximum speedup factor of 1208.27. The low-dissipation property of the scheme is further assessed through the inviscid Taylor-Green vortex problem. Finally, a series of challenging three-dimensional benchmark cases demonstrate that the present scheme achieves high accuracy, low dissipation, and excellent computational efficiency in simulating strongly compressible flows with complex features such as strong shock waves and discontinuities.