Effects of Numerical Dissipation and Dispersion on Computing the Convection of a Sharp Scalar Cone

Abstract

AbstractThis work presents a classical study on the numerical-dissipation and dispersion behaviors of upwind and central space-discretization schemes. For this purpose, pure convection of a sharp scalar cone is simulated by numerically solving the two-dimensional convection-diffusion equation with zero physical diffusion. The velocity field is so chosen that the scalar cone rotates about the origin. The numerical solutions are carried out on the finite-volume framework, where the interface fluxes are approximated by the first-order upwind (FOU), second-order central difference (CDS2), and Quadratic Upstream Interpolation for Convective Kinematics (QUICK) schemes. Although in the absence of physical dissipation, the cone should rotate without any decay of its amplitude, it is found that the different numerical-flux schemes result in different declining rates of amplitude. This is attributed to different levels of numerical dissipation of the schemes. In addition, it is seen that the numerical dispersions of the schemes result in the change of phase of the scalar being convected, yielding spurious numerical oscillations. The present study compares the FOU, CDS2, and QUICK schemes in the finite-volume computation of the convection-diffusion equation vis-à-vis their numerical dissipation and dispersion. The study demonstrates that among the lot, the FOU scheme is the most dissipative and the QUICK scheme is the least dissipative. On the other hand, the CDS2 scheme is the most dispersive. The aforementioned observations with the FOU and CDS2 schemes are substantiated with finite-difference computation of the governing equation using these schemes for approximating the space derivatives.KeywordsConvection-diffusion equationNumerical dissipationNumerical dispersion