Further improvement and analysis of CCD scheme: Dissipation discretization and de-aliasing properties

In this paper, we further analyze a combined compact difference (CCD) scheme proposed recently T.K. Sengupta, V. Lakshmanan, V.V.S.N. Vijay, A new combined stable and dispersion relation preserving compact scheme for non-periodic problems, J. Comput. Phys. 228 (8) (2009) 3048–3071] for its dissipation discretization properties to show that its superiority also helps in controlling aliasing error for a benchmark internal flow. However, application of the same CCD method to study the receptivity of a boundary layer experiencing adverse pressure gradient is not successful. This is traced to the nature of the equilibrium flow where the better dissipation property is not helpful in the inviscid part of the flow, where the aliasing problems continue to persist. A further modification is proposed to the CCD method here to solve complex physical problems requiring information on higher order disturbance quantities – as in problems of flow receptivity and instability.