A new point-centered diffusion differencing for unstructured meshes

Conference · Tue Jan 18 04:00:00 EST 1994

OSTI ID:10120949

Palmer, T. S. ^[1]

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1. Lawrence Livermore National Lab., CA (United States)

During the last few years, there has been an increased effort to devise robust transport differencings for unstructured meshes, specifically arbitrarily connected grids of polygons. Conversely, development of diffusion methods on these grids has been lacking. While Morel, Kershaw, Shestakov and others have done a great deal of work on diffusion schemes for logically-rectangular grids, to our knowledge there has been little or no work on discretizations of the diffusion equation on unstructured meshes of polygons. In this paper, we introduce a point-centered diffusion differencing for general two-dimensional unstructured meshes. The method has the following attractive properties: (1) transition to the standard five-point point-centered scheme on orthogonal meshes; (2) preservation of the homogeneous linear solution; (3) second-order accuracy; (4) strict conservation within the control volume surrounding each point; and (5) convergence to the exact result as the mesh is refined, regardless of the smoothness of the mesh. The only potential disadvantage of the method is that the diffusion matrix is asymmetric, in general.

• Research Organization: Lawrence Livermore National Lab., CA (United States)
• Sponsoring Organization: USDOE, Washington, DC (United States)
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 10120949
• Report Number(s): UCRL-JC--116063; CONF-940630--3; ON: DE94006399
• Country of Publication: United States
• Language: English

Related Subjects

663610
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
99 GENERAL AND MISCELLANEOUS
990200
FINITE ELEMENT METHOD
MATHEMATICS AND COMPUTERS
MESH GENERATION
NEUTRON DIFFUSION EQUATION
NEUTRON PHYSICS