A nodal discontinuous Galerkin method for computational aeroacoustics and comparison with finite difference schemes

Abstract

A nodal discontinuous Galerkin formulation, which is based on Lagrange polynomials basis, is used to directly simulate the acoustic wave propagation. Two test problems of wave propagation with initial disturbance consisting of a Gaussian profile or rectangular pulse are investigated. We evaluate the performance of the schemes in short, intermediate, and long waves. Moreover, the comparisons of numerical results between the nodal discontinuous Galerkin method and finite difference type schemes are performed, which indicate that the numerical solution obtained using nodal discontinuous Galerkin method with a pure central flux has obvious high frequency oscillations for initial disturbance consisting of rectangular pulse, which is the same as those obtained using finite difference type schemes without artificial selective damping. If an upwind flux is adopted, spurious waves are eliminated effectively except for the location of discontinuities. When a limiter is used, obviously the spurious short waves are almost completely removed. The quality of the computed solution has greatly improved.