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

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-diffusivity. 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 different combinations of the BFECC algorithms and the underlying numerical schemes. Results are presented for both the structured and unstructured meshes. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

In this paper, the BFECC methodology is used to improve solvers for the advection equation. The algorithm enforces a discrete maximum principle and improves accuracy by introducing controlled anti-diffusivity. The proposed methodology is assessed using benchmark tests on structured and unstructured meshes.