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Divergence preserving reconstruction of the nodal components of a vector field from its normal components to edges

Journal Article · · International Journal for Numerical Methods in Fluids
DOI:https://doi.org/10.1002/fld.4289· OSTI ID:1492600
 [1];  [2]
  1. Czech Technical Univ., Prague (Czech Republic). Faculty of Nuclear Sciences and Physical Engineering
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
+ Show Author Affiliations
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. Here in this paper, we describe all details of our new method and present numerical results, which confirm our theory.
Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
89233218CNA000001
OSTI ID:
1492600
Report Number(s):
LA-UR--15-23646
Journal Information:
International Journal for Numerical Methods in Fluids, Journal Name: International Journal for Numerical Methods in Fluids Journal Issue: 10 Vol. 83; ISSN 0271-2091
Publisher:
WileyCopyright Statement
Country of Publication:
United States
Language:
English

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Figures / Tables (9)

Figure 1(p. 3)figure Figure 1
Figure 2(p. 4)figure Figure 2
Figure 3(p. 6)figure Figure 3
Figure 4(p. 8)figure Figure 4
Figure 5(p. 9)figure Figure 5
Figure 6(p. 11)figure Figure 6
Table I(p. 12)table Table I
Table II(p. 12)table Table II
Table III(p. 13)table Table III

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Divergence preserving vector field reconstruction
Lagrangian
divergence preserving
finite difference
hydrodynamics
vector interpolation
vector representation