Abstract
We consider, for this contribution, the cell-centered finite volume method based on least squares vertex reconstruction. This method, which is also popularly known as “the diamond scheme”, was originally presented for the advection-diffusion equation in two-dimensions and then extended in 3-D.
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Bertolazzi, E., Manzini, G.: A cell-centered second-order accurate finite volume method for convection-diffusion problems on unstructured meshes. Math. Models Methods Appl. Sci. 8, 1235–1260 (2004)
Bertolazzi, E., Manzini, G.: On vertex reconstructions for cell-centered finite volume approximations of 2-D anisotropic diffusion problems. Math. Models Methods Appl. Sci. 17(1), 1–32 (2007)
Coudière, Y.: Analyse de schémas volumes finis sur maillages non structurés pour des problèmes linéaires hyperboliques et elliptiques. Ph.D. thesis, Universitè "P. Sabatier" de Toulouse, Toulouse III, Toulouse, France (1999)
Coudière, Y., Vila, J.P., Villedieu, P.: Convergence rate of a finite volume scheme for a two-dimensional diffusion convection problem. M2AN, Math. Model. Numer. Anal. 33(3), 493–516 (1999)
Coudière, Y., Villedieu, P.: Convergence of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes. M2AN, Math. Model. Numer. Anal. 34(6), 1123–1149 (2000)
Manzini, G., Putti, M.: Mesh locking effects in the finite volume solution of 2-D anisotropic diffusion equations. J. Comput. Phys. 220(2), 751–771 (2007)
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© 2011 Springer-Verlag Berlin Heidelberg
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Coudière, Y., Manzini, G. (2011). Benchmark 3D: The Cell-Centered Finite Volume Method Using Least Squares Vertex Reconstruction (“Diamond Scheme”). In: Fořt, J., Fürst, J., Halama, J., Herbin, R., Hubert, F. (eds) Finite Volumes for Complex Applications VI Problems & Perspectives. Springer Proceedings in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20671-9_96
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DOI: https://doi.org/10.1007/978-3-642-20671-9_96
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