IMPROVED HESSIAN RECONSTRUCTION SCHEME FOR CELL-CENTRED FINITE VOLUME METHOD

摘要

A simple and accurate least-square Hessian recon- struction scheme is proposed for the cell-centered finite volume method on structured or unstructured grids. The target application of the proposed scheme is in grid adaptation. The novelty of the scheme is the capability to provide more accurate estimates for the gradient and Hessian on a compact computational molecule. The scheme is developed and tested in the two-dimensional context; however, one can easily ex- tend it to three-dimensional problems. The results for the transport of a scalar show remarkable improve- ments in the estimated gradient and Hessian on non- orthogonal grids.