期刊
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
卷 69, 期 12, 页码 1872-1890出版社
WILEY-BLACKWELL
DOI: 10.1002/fld.2669
关键词
geometric conservation law; ALE formulation; moving meshes; finite element method
类别
资金
- Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET, Argentina) [PIP 5271/05]
- Universidad Nacional del Litoral (UNL, Argentina) [CAI+D 2009 65/334]
- Agencia Nacional de Promocion Cientifica y Tecnologica (ANPCyT, Argentina) [PICT 01141/2007, PICT 2008-0270, PICT 1506/2006]
In this article, a new methodology for developing discrete geometric conservation law (DGCL) compliant formulations is presented. It is carried out in the context of the finite element method for general advectivediffusive systems on moving domains using an ALE scheme. There is an extensive literature about the impact of DGCL compliance on the stability and precision of time integration methods. In those articles, it has been proved that satisfying the DGCL is a necessary and sufficient condition for any ALE scheme to maintain on moving grids the nonlinear stability properties of its fixed-grid counterpart. However, only a few works proposed a methodology for obtaining a compliant scheme. In this work, a DGCL compliant scheme based on an averaged ALE Jacobians formulation is obtained. This new formulation is applied to the ? family of time integration methods. In addition, an extension to the three-point backward difference formula is given. With the aim to validate the averaged ALE Jacobians formulation, a set of numerical tests are performed. These tests include 2D and 3D diffusion problems with different mesh movements and the 2D compressible NavierStokes equations. Copyright (c) 2011 John Wiley & Sons, Ltd.
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