We propose a unified treatment of internal and boundary vertex least-squares reconstructions in second-order accurate cell-centered finite-volume discretisation of 2-D steady diffusion problems. Dirichlet, Neumann, and Robin boundary conditions are taken into account in the same formulation by introducing suitable constraints in the least-squares minimization process. The method is discussed in its theoretical framework and a representative numerical experiment illustrates its capability in providing the second-order of accuracy. © 2005 Elsevier Ltd. All rights reserved.
A unified treatment of boundary conditions in least-square based finite-volume methods
Bertolazzi, Enrico;
2005-01-01
Abstract
We propose a unified treatment of internal and boundary vertex least-squares reconstructions in second-order accurate cell-centered finite-volume discretisation of 2-D steady diffusion problems. Dirichlet, Neumann, and Robin boundary conditions are taken into account in the same formulation by introducing suitable constraints in the least-squares minimization process. The method is discussed in its theoretical framework and a representative numerical experiment illustrates its capability in providing the second-order of accuracy. © 2005 Elsevier Ltd. All rights reserved.File in questo prodotto:
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