Block Interface Flux Reconstruction Method with Nonlinear Scheme for Aeroacoustics Problem

Nonconforming grids, which can simplify the generation of meshes for complex shapes and reduce the number of meshes, are commonly employed in addressing multiscale aeroacoustics numerical simulation challenges. This approach allows for the simulation of sound propagation processes at a reasonable cost. By utilizing the sixth-order weighted compact nonlinear hybrid scheme (WCNHS) with a piecewise exponential mapping function (WCNHS_Pe) and incorporating ghost grid blocks, a method has been developed to reconstruct interface flux for nonsingle-scale multiblock structured grids. The variable values of the ghost grid at the grid boundary are determined through high-order optimization interpolation methods. Furthermore, different time steps can be implemented for each subdomain to accommodate corresponding grid scales. To address coupling across multiple grid sizes, an interface flux reconstruction method is applied to numerically simulate various scenarios, including Sod shock tube problem, the Shu–Osher problem, Gaussian pulse propagation on two-dimensional nonconforming grids, sound propagation on discontinuous interfaces, sound radiation from three cylinders, sound generated by weak shock–vortex interaction, Gaussian pulse propagation on three-dimensional nonconforming grids, and slat noise prediction. The results demonstrate that the high-order finite difference method established in this study exhibits superior capability in capturing discontinuities as well as higher resolution and lower dispersion on nonconforming multisize meshes, making it suitable for simulating linear and nonlinear acoustic problems.