Development of a high-resolution hyperbolic model on quadratic elements

Abstract

This paper presents a class of Taylor–Galerkin (TG) finite element models on quadratic elements for solving a pure convection equation which admits discontinuities. Six parameters are introduced to preserve scheme monotonicity and control solution accuracy. In this paper we apply the M-matrix theory in the construction of monotone TG model. To avoid making the scheme overly diffusive, the flux-corrected transport (FCT) technique of Boris and Book is applied together with the underlying entropy-increasing principle and modified equation analysis developed for the TG models. Reduction of post-discontinuities is the direct use of free parameters that can make the coefficients of the even and odd derivative terms shown in the modified equation change signs alternately. Several benchmark problems are investigated to confirm the integrity of the proposed characteristic model.