A conservative finite volume method for the variable-coefficient linearized Euler equations in aeroacoustics

Under complex geometries and non-uniform media, weakly compressible aeroacoustic prediction requires methods that balance amplitude–phase accuracy with numerical stability. Because direct simulations of the fully compressible Navier–Stokes equations are prohibitively expensive and involve strong coupling between unsteady flow and acoustic perturbations, we develop a weakly compressible aeroacoustic solver within the finite-volume framework of OpenFOAM. For variable-coefficient LEE, a face-centered Roe-averaged, consistent eigendecomposition is introduced to construct a single-face, uniquely conservative Roe flux, together with an explicit fourth-order Runge–Kutta (RK4) time integration. At the outer boundaries, characteristic non-reflecting boundary conditions (NRBCs) are combined with a sponge damping layer to reduce numerical reflections of outgoing waves. Benchmark tests demonstrate accurate reproduction of canonical propagation phenomena, including convection/pulse propagation and rigid-wall reflection. The solver maintains good amplitude–phase consistency for two- and three-dimensional point-source radiation and for refraction in shear mean flows, while substantially suppressing boundary reflections. Highly consistent results across different mesh topologies indicate strong mesh generality and engineering robustness. Finally, the NACA 0012 airfoil case shows radiated-field features and one-third-octave-band spectra in good agreement with reference experimental data, confirming the feasibility of the proposed solver.