On the development of a dispersion-relation-preserving dual-compact upwind scheme for convection–diffusion equation

In this paper a dual-compact scheme, which accommodates a better dispersion relation for the convective terms shown in the transport equation, is proposed to enhance the convective stability of the convection–diffusion equation by virtue of the increased dispersive accuracy. The dispersion-relation-preserving compact scheme has been rigorously developed within the three-stencil point framework through the dispersion and dissipation analyses. To verify the proposed method, several problems that are amenable to the exact and benchmark solutions will be investigated. The results with good rates of convergence are demonstrated for all the investigated problems.