Divergence preserving reconstruction of the nodal components of a vector field from its normal components to edges. (22nd August 2016)

• Record Type: Journal Article
• Authors: Liska, Richard; Shashkov, Mikhail
• Is Part Of: International journal for numerical methods in fluids. Volume 83:Number 10(2017)
• Page Start: 798
• Page End: 809
• Publication Date: 2016-08-22
• Subjects: Lagrangian -- hydrodynamics -- vector interpolation -- divergence preserving -- vector representation -- finite difference; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4289
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: We have developed a new divergence preserving method for the reconstruction of the Cartesian components of a vector field from the orthogonal projection of a vector field to the normals to edges in two dimensional. In this method, discrete divergences computed from the nodal components and from the normal ones are exactly the same. Our new method consists of two stages. At the first stage, we use an extended version of the local procedure described in [ J. Comput. Phys., 139 :406–409, 1998] to obtain a 'reference' nodal vector. This local procedure is exact for linear vector fields; however, the discrete divergence is not preserved. Then, we formulate a constrained optimization problem, in which this reference vector plays the role of a target, and the divergence constraints are enforced by using Lagrange multipliers. It leads to the solution of 'elliptic' like discrete equations for the cell‐centered Lagrange multipliers. The new global divergence preserving method is exact for linear vector fields. We describe all details of our new method and present numerical results, which confirm our theory. Copyright © 2016 John Wiley & Sons, Ltd. Abstract : We have developed a new divergence preserving method for the reconstruction of the Cartesian components of a vector field from the orthogonal projection of a vector field to the normals to edges in 2D. The new global divergence preserving method is exact for linear vector fields.