Kernel-based vector field reconstruction in computational fluid dynamic models

被引:16
作者
Bonaventura, L. [1 ]
Iske, A. [2 ]
Miglio, E. [1 ]
机构
[1] Politecn Milan, Dipartimento Matemat F Brioschi, MOX Modellist & Calcolo Sci, I-20133 Milan, Italy
[2] Univ Hamburg, Dept Math, D-20146 Hamburg, Germany
关键词
kernel-based approximation methods; local vector field reconstruction; Raviart-Thomas (RT) elements; computational fluid dynamics; SHALLOW-WATER EQUATIONS; SEMI-LAGRANGIAN ADVECTION; FINITE-VOLUME METHODS; POTENTIAL ENSTROPHY; OPTIMAL RECOVERY; SCHEME; APPROXIMATION; INTERPOLATION; SEMIIMPLICIT; MESHES;
D O I
10.1002/fld.2279
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
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. Copyright (C) 2010 John Wiley & Sons, Ltd.
引用
收藏
页码:714 / 729
页数:16
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