Efcient 3rd-Order Finite-Volume Discretization Using Iterative Quadratic Data Reconstruction on Unstructured Grids.

Although higher than 2nd-order accurate nite-volume discretizations on unstructured-grids have already been proposed, the approach has not yet gained much popularity. This is due to the high computational cost and memory requirements of the proposed schemes and to the technical difculties in achieving a high-order accurate solution, especially when considering ow in complex geometries. In this paper we detail a 3rd-order cell-centred nite-volume discretization based on quadratic data recov-ery, which is computationally efcient and has optimal memory requirements. The density-based ow-solver discretization and solution algorithm are described briey, followed by a detailed presentation of the least-squares based iterative quadratic data reconstruction methodology we propose. We conclude our paper with numerical examples to verify the accuracy and numerical efciency of our high-order nite-volume discretiza-tion. I