An enhanced non-oscillatory BFECC algorithm for finite element solution of advective transport problems

Abstract

In this paper, the so-called “back and forth error compensation correction (BFECC)” methodology is utilized to improve the solvers developed for the advection equation. Strict obedience to the so-called “discrete maximum principle” is enforced by incorporating a gradient–based limiter into the BFECC algorithm. The accuracy of the BFECC algorithm in capturing the steep–fronts in hyperbolic scalar–transport problems is improved by introducing a controlled anti–di¿usivity. This is achieved at the cost of performing an additional backward sub–solution–step and modifying the formulation of the error compensation accordingly. The performance of the proposed methodology is assessed by solving a series of benchmarks utilizing di¿erent combinations of the BFECC algorithms and the underlying numerical schemes. Results are presented for both the structured and unstructured meshes.