Kernel‐based vector field reconstruction in computational fluid dynamic models

TL;DR: The proposed kernel‐based reconstruction improves the accuracy of standard finite element discretizations, including Raviart–Thomas (RT) elements, quite significantly, while retaining discrete conservation properties of important physical quantities, such as mass, vorticity, or potential enstrophy.

Abstract: Kernel-based reconstruction methods are applied to obtain highly accurate approximations of local vector fields from normal components assigned at the edges of a computational mesh The theoretical background of kernel-based reconstructions for vector-valued functions is first reviewed, before the reconstruction method is adapted to the specific requirements of relevant applications in computational fluid dynamics To this end, important computational aspects concerning the design of the reconstruction scheme like the selection of suitable stencils are explained in detail Extensive numerical examples and comparisons concerning hydrodynamic models show that the proposed kernel-based reconstruction improves the accuracy of standard finite element discretizations, including Raviart―Thomas (RT) elements, quite significantly, while retaining discrete conservation properties of important physical quantities, such as mass, vorticity, or potential enstrophy