Abstract
We study in this paper a model problem of advection diffusion type on a region which contains a subregion where it is sufficient to approximate the problem by the pure advection equation. We define coupling conditions at the interface between the two regions which lead to a coupled solution which approximates the fully viscous solution more accurately than other conditions from the literature, and we develop a fast algorithm to solve the coupled problem.
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References
E. Dubach, Contribution a la résolution des equations fluides en domaine non borné, PhD thesis, Universite Paris 13, Fevrier 1993.
O. Dubois, Optimized Schwarz methods for the advection-diffusion equation, Master's thesis, McGill University, 2003.
M. J. Gander, L. Halpern, and C. Japhet, Optimized Schwarz algorithms for coupling convection and convection-diffusion problems, in Thirteenth international conference on domain decomposition, N. Debit, M. Garbey, R. Hoppe, J. Périaux, D. Keyes, and Y. Kuznetsov, eds., ddm.org, 2001, pp. 253–260.
F. Gastaldi, A. Quarteroni, and G. S. Landriani, On the coupling of twodimensional hyperbolic and elliptic equations: analytical and numerical approach, in Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, held in Houston, Texas, March 20–22, 1989, T. F. Chan, R. Glowinski, J. Périaux, and O. Widlund, eds., Philadelphia, PA, 1990, SIAM, pp. 22–63.
C. Japhet, Méthode de décomposition de domaine et conditions aux limites arti ficielles en mécanique des fluides: méthode optimisée d'ordre 2, PhD thesis, Université Paris 13, 1998.
A. Quarteroni and A. Valli, Domain Decomposition Methods for Partial Differential Equations, Oxford University Press, 1999.
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Gander, M.J., Halpern, L., Japhet, C., Martin, V. (2007). Advection Diffusion Problems with Pure Advection Approximation in Subregions. In: Widlund, O.B., Keyes, D.E. (eds) Domain Decomposition Methods in Science and Engineering XVI. Lecture Notes in Computational Science and Engineering, vol 55. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34469-8_26
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DOI: https://doi.org/10.1007/978-3-540-34469-8_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34468-1
Online ISBN: 978-3-540-34469-8
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