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-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.
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