A comparison of TVD limiter functions for a convection-diffusion-reaction equation and Euler equations on triangular grids

摘要

The spatial reconstruction is an essential process for the finite volume method to create the left and right states at the cell face of each control volume for the second- or higher-order accurate schemes. The gradient quantities used by the reconstruction process usually cause the scheme to generate oscillations and spurious solutions across discontinuities. The one-dimensional analysis indicates that the scheme is stable with second-order accuracy. In this paper, we aim to compare the stability and accuracy of the TVD limiter functions applied to the characteristic-based finite volume element method (CFVEM) for solving the convection-diffusion-reaction (CDR) equation on two-dimensional triangular grids. The Barth Jespersen, Venkatakrishnan, and some well-known TVD limiters, including TVD-Superbee, TVD-Minmod, TVD-MUSCL, and TVD-Koren, are selected for the comparison. The new Sweby's r-factor of TVD limiters based on the upwind concept is introduced. The accuracy and stability of the limiters are examined by solving several pure convection and convection-diffusion-reaction problems on both structured and unstructured triangular grids. The limiters are further applied to solve Euler equations. It is found that they give impressive results for both linear and nonlinear problems.