A high-order flux reconstruction solver of the linearized Euler equation for acoustic wave propagation

This paper presents a high-order flux reconstruction solver for the linearized Euler equations, developed to accurately simulate acoustic wave propagation in complex media. The solver utilizes polynomial-based approximations to construct the local solution and employs correction functions for flux-derivative reconstruction. Temporal integration is performed using a five-stage, fourth-order Runge–Kutta scheme. The solver also incorporates automatic derivative computation for the mean flow fields using the polynomial approximation. Numerical tests confirm that the solver achieves the expected (p+1)-th order convergence rate, where p is the polynomial order. A series of benchmark problems illustrates the framework's efficiency in handling unstructured meshes, complex boundary conditions, acoustic scattering in non-uniform flows, flow-induced noise, and large-scale parallel computations. Further analyses of shear-flow cases demonstrate the solver's ability in mitigating numerical instabilities and underscore the importance of choosing suitable equation formulations based on flow characteristics.