Abstract：Numerical schemes that have minimal dispersion and dissipation errors are desired for direct simulation of noise propagation. Dispersion and dissipation properties of nodal discontinuous Galerkin(DG) method for the linearized Euler equation are investigated by utilizing an eigenvalue analysis technique. It is found that for any given order of the basis functions, there are m+1 mode of numerical waves. But only one represents propagating mode of physical wave corresponding to the partial differential equations, the rest are numerical parasite modes. The directions of propagation of these two numerical modes are opposite. Moreover, the comparisons of dispersion properties among the nodal discontinuous Galerkin method, DRP schemes and compact finite difference schemes with the same order show the solvable wavenumber range lying between DRP schemes and compact finite difference schemes. Finally, a test problem of wave propagation with initial disturbance consisting of a Gaussian profile is solved. The quality of solution obtained by nodal DG method with less grid number are analogous to that of compact finite difference schemes, but better than that of DRP schemes, which indicate this method is very appropriate to direct numerical simulation of aeroacoustics.
2012, Vol. 31 
