A transport-physics-accurate convection discretization based on first order upwind and the need for a new error assessment strategy

Abstract

Several numerical schemes have been proposed in the literature to deal with convection phenomena, but all of them present some spurious effects. In this paper we show that, once a more physically-oriented error assessment tool is used in substitution for the classical wave number analysis, it is possible to develop an improved family of numerical schemes. Results are presented for a particular implementation based on first order upwind, in test cases involving linear and non-linear convective equation. This new scheme is able to simulate linear convection equation under uniform field with machine accuracy precision, with zero diffusion and dispersion. Moreover, the results for the non-linear convection are also significantly more accurate over the whole spectrum when compared to a traditional scheme based on a fifteen points stencil.