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Higher-Order Linear-Time Unconditionally Stable Alternating Direction Implicit Methods for Nonlinear Convection-Diffusion Partial Differential Equation Systems

Bruno, Oscar P. and Jimenez, Edwin (2014) Higher-Order Linear-Time Unconditionally Stable Alternating Direction Implicit Methods for Nonlinear Convection-Diffusion Partial Differential Equation Systems. Journal of Fluids Engineering, 136 (6). Art. No. 060904 . ISSN 0098-2202. http://resolver.caltech.edu/CaltechAUTHORS:20140612-100139439

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Abstract

We introduce a class of alternating direction implicit (ADI) methods, based on approximate factorizations of backward differentiation formulas (BDFs) of order p≥2, for the numerical solution of two-dimensional, time-dependent, nonlinear, convection-diffusion partial differential equation (PDE) systems in Cartesian domains. The proposed algorithms, which do not require the solution of nonlinear systems, additionally produce solutions of spectral accuracy in space through the use of Chebyshev approximations. In particular, these methods give rise to minimal artificial dispersion and diffusion and they therefore enable use of relatively coarse discretizations to meet a prescribed error tolerance for a given problem. A variety of numerical results presented in this text demonstrate high-order accuracy and, for the particular cases of p=2,3, unconditional stability.


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http://dx.doi.org/10.1115/1.4026868 DOIArticle
http://fluidsengineering.asmedigitalcollection.asme.org/article.aspx?articleid=1868761PublisherArticle
Additional Information:© 2014 by ASME. Contributed by the Fluids Engineering Division of ASME for publication in the Journal of Fluids Engineering. Manuscript received December 2, 2013; final manuscript received January 29, 2014; published online April 28, 2014. Assoc. Editor: Ye Zhou. The authors gratefully acknowledge support by the Air Force Office of Scientific Research and the National Science Foundation. We are also thankful for a number of useful comments from the reviewers, which have helped improve the quality of this presentation.
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Record Number:CaltechAUTHORS:20140612-100139439
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20140612-100139439
Official Citation:J. Fluids Eng. 136, 060904 (2014) (7 pages); Paper No: FE-13-1695; doi:10.1115/1.4026868
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:46234
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:12 Jun 2014 19:22
Last Modified:12 Jun 2014 19:22

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