We introduce a new spatial discretization scheme for transport on arbitrary spatial grids in XY geometry. Our arbitrary'' spatial grid is composed of arbitrarily-connected polygons, each of which may have an arbitrary number of sides. We begin our derivation by imposing particle balance on every corner'' of each cell (Consequently, we call our scheme the corner-balance (CB) method.) We complete the derivation by introducing simple closure formulas that relate volume-averaged unknowns to surface-averaged unknowns in each corner. We discuss the relationship of the new scheme to discontinuous finite-element methods and to multiple-balance methods. We demonstrate that on simple grids, the …
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We introduce a new spatial discretization scheme for transport on arbitrary spatial grids in XY geometry. Our arbitrary'' spatial grid is composed of arbitrarily-connected polygons, each of which may have an arbitrary number of sides. We begin our derivation by imposing particle balance on every corner'' of each cell (Consequently, we call our scheme the corner-balance (CB) method.) We complete the derivation by introducing simple closure formulas that relate volume-averaged unknowns to surface-averaged unknowns in each corner. We discuss the relationship of the new scheme to discontinuous finite-element methods and to multiple-balance methods. We demonstrate that on simple grids, the method reduces to very robust schemes that have been studied previously. We discuss the theoretical performance of the method in the thick diffusion limit, and provide numerical results for that limit. We present additional numerical results from simple problems that test the new scheme in other limits. Finally, we offer some concluding remarks about the method. 9 refs., 6 figs.
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Adams, M.L.A new transport discretization scheme for arbitrary spatial meshes in XY geometry,
article,
January 18, 1991;
[Livermore,] California.
(https://digital.library.unt.edu/ark:/67531/metadc1114137/:
accessed May 22, 2024),
University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu;
crediting UNT Libraries Government Documents Department.
