Accuracy Enhancing Interface Treatment Algorithm: The Back and Forth Error Compensation and Correction Method

Abstract

The accuracy of information transmission while solving domain decomposed problems is crucial to the smooth transition of a solution around the interface/overlapping region. This paper describes a systematical study on an accuracy-enhancing interface treatment algorithm based on the back and forth error compensation and correction method (BFECC). By repetitively employing a low order interpolation technique (usually local 2nd order) 3 times, this algorithm achieves local 3rd order accuracy. Analytical derivation for any dimensions is made, and the “superconvergence” phenomenon (4th order accuracy) is found for specific positioning of the source and target grids. Its limitation has also been studied. With rotated grids or grids of different sizes, this method can still reduce the error but fails to improve the order of the underlying interpolation technique. A series of numerical experiments on meshes with various translations, rotations, spacing ratios, and perturbations have been tested. Different interface treatments applied to cavity flow are compared. The 3D flow example shows that the BFECC method positively impacts the convergence of the domain decomposed problem.