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

https://doi.org/10.1016/j.cma.2022.114576Get rights and content
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Highlights

  • BFECC-based methodology to increase the order of accuracy for transport problems.

  • Non-iterative algorithm with a predictable computational cost (fixed number of steps).

  • Adjustment of the extra (anti-)diffusion of various stabilized schemes.

  • Monotonicity preservation via incorporation of a gradient-based limiter.

  • Proposal for improving BFECC in the presence of local extrema.

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.

Keywords

Convection-dominated transport
BFECC
Limiter
Monotonicity preservation
Discrete maximum principle

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