An efficient quadratic interpolation scheme for a third-order cell-centered finite-volume method on tetrahedral grids

In this paper, we propose an efficient quadratic interpolation formula utilizing solution gradients computed and stored at nodes demonstrate its application to a third-order cell-centered finite-volume discretization on tetrahedral grids. The proposed is constructed based of computing projected derivative. It in that it completely eliminates the need compute store second derivatives variables or any other quantities, which are typically required upgrading second-order unstructured-grid accuracy. Moreover, high-order flux quadrature formula, as for accuracy, can also be simplified by projected-derivative resulting numerical face centroid plus curvature correction not involving flux. Similarly, source term integrated over cell form evaluated correction, again, requiring term. defined approximation integral conservation law but point value center, leading another feature there no geometric moments polynomial preserve average. Third-order accuracy improved demonstrated investigated simple illustrative test cases three dimensions.