Parabolic approximations of the convection-diffusion equation
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- by J.-P. Lohéac, F. Nataf and M. Schatzman PDF
- Math. Comp. 60 (1993), 515-530 Request permission
Abstract:
We propose an approximation of the convection-diffusion operator which consists in the product of two parabolic operators. This approximation is much easier to solve than the full convection-diffusion equation, which is elliptic in space. We prove that this approximation is of order three in the viscosity and that the classical parabolic approximation is of order one in the viscosity. Numerical examples are given to demonstrate the effectiveness of our new approximation.References
- G. K. Batchelor, An introduction to fluid dynamics, Second paperback edition, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1999. MR 1744638 P. C. Chatwin and C. M. Allen, Mathematical models of dispersion in rivers and estuaries, Ann. Rev. Mech. 17 (1985), 119-149.
- Laurence Halpern, Artificial boundary conditions for the linear advection diffusion equation, Math. Comp. 46 (1986), no. 174, 425–438. MR 829617, DOI 10.1090/S0025-5718-1986-0829617-8 O. A. Ladyženskaya, V. A. Solonnikov, and N. N. Ural’ceva, Linear and quasi-linear equations of parabolic type, Transl. Math. Monographs, vol. 23, Amer. Math. Soc., Providence, RI, 1968. J. L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Dunod, Paris, 1968.
- Jean-Pierre Lohéac, An artificial boundary condition for an advection-diffusion equation, Math. Methods Appl. Sci. 14 (1991), no. 3, 155–175. MR 1099323, DOI 10.1002/mma.1670140302 F. Nataf, Paraxialisation des équations de Navier-Stokes, Rapport Interne CMAP, Janvier 1988. —, Approximation paraxiale pour les fluides incompressibles. Etude mathématique et numérique, Thèse de doctorat de l’Ecole Polytechnique, 1989.
- Hermann Schlichting, Boundary layer theory, McGraw-Hill, New York; Pergamon Press, London; Verlag G. Braun, Karlsruhe, 1955. Translated by J. Kestin. MR 0076530 B. D. Spalding, Imperial College Mech. Eng. Dept. Report HTS/75/5, 1975. W. S. Vorus, A theory for flow separation, J. Fluid Mech. 132 (1983), 163-183.
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Math. Comp. 60 (1993), 515-530
- MSC: Primary 65N06; Secondary 65N15, 76M20, 76R99
- DOI: https://doi.org/10.1090/S0025-5718-1993-1160276-7
- MathSciNet review: 1160276