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.