Spurious waves in discrete computation of wave phenomena and flow problems

In the present work, we focus on spurious propagating disturbances (q-waves). To establish the existence of q-waves in computations, we compare properties of different numerical methods drawn from finite difference, finite volume and finite element methods. Existence and properties of q-waves are demonstrated with propagation of wave-packets following one-dimensional (1D) convection equation; skewed wave propagation and by solution of linearized rotating shallow water wave equation (LRSWE). Specific numerical experiments are performed with parameters that convert a wave-packet into a q-wave. We also show the case where q-waves are created additionally to physical disturbances those propagate downstream. Formation of q-waves are shown in the case of a discrete shielded vortex in the uniform flow and incompressible transitional flow past an aerofoil by solving the Navier-Stokes equation. In performing this exercise, we establish critical wavenumber range beyond which q-waves are created. Relevance of this information for DNS and LES is discussed. We have further discussed the case of spurious caustics in discrete computing. (C) 2012 Elsevier Inc. All rights reserved.