IMPLICIT FACTORIZATION TECHNIQUES FOR TWO-DIMENSIONAL, ANISOTROPIC, REACTIVE–DIFFUSIVE MEDIA WITH CROSS-DIFFUSION EFFECTS

Abstract

International Journal of Computational Engineering ScienceVol. 05, No. 03, pp. 681-697 (2004) No AccessIMPLICIT FACTORIZATION TECHNIQUES FOR TWO-DIMENSIONAL, ANISOTROPIC, REACTIVE–DIFFUSIVE MEDIA WITH CROSS-DIFFUSION EFFECTSJ. I. RAMOSJ. I. RAMOSE. T. S. Ingenieros Industriales, Universidad de Málaga, Plaza El Ejido, s/n, 29013 Málaga, Spain Search for more papers by this author https://doi.org/10.1142/S1465876304002630Cited by:1 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractThe propagation of fronts in two–dimensional, anisotropic, nonlinear reactive–diffusive media with cross–diffusion is analyzed by means of implicit time–linearized factorization techniques. Four factorization methods are considered; the first one disregards the approximate factorization errors and treats the mixed second–order derivatives explicitly, whereas the other three account for either the approximate factorization errors or the mixed second–order derivative terms in an iterative manner. The four techniques involve the solution of one–dimensional operators and require the solution of linear algebraic systems with block–tridiagonal matrices. It is shown that anisotropy and cross–diffusion deform the reaction front and affect the front velocity. It is also shown that the approximate factorization method that treats the mixed second–order derivative terms iteratively provide much more accurate transient results than techniques that account for the approximate factorization errors and treat the mixed second–order derivative terms in an explicit manner.Keywords:Anisotropic mediareaction–diffusion equationslinearization methodsapproximate factorization References S. Pietruszczak, D. Lydzba and J. F. Shao, Int. J. Solids & Structures 39, 637 (2002). Crossref, Google ScholarE. Uhlmannet al., Int. J. Machine Tools & Manufacture 39, 639 (1999). Crossref, Google ScholarC. T. Pan and H. Hocheng, J. Materials Processing Tecnology 62, 54 (1996). Crossref, Google ScholarP. Bera and A. Khalili, Int. J. Heat Mass Transfer 45, 3205 (2002). Crossref, Google ScholarG. Degan, S. Zohoun and P. Vasseur, Int. J. Heat Mass Transfer 45, 3181 (2002). Crossref, Google ScholarB. Yang and E. Pan, Engineering Analysis with Boundary Elements 26, 355 (2002). Crossref, Google ScholarM.-H. Hsieh and C.-C. Ma, Int. J. Heat Mass Transfer 45, 4117 (2002). Crossref, Google ScholarF. Kowsary and M. Arabi, Int. Comm. Heat Mass Transfer 26, 1163 (1999). Crossref, Google ScholarF. M. L. Traiano, R. M. Cotta and H. R. B. Orlande, Int. Comm. Heat Mass Transfer 24, 869 (1997). Crossref, Google ScholarS. Yi, H. H. Hilton and M. F. D. Ahmad, Computers & Structures 64, 383 (1997). Crossref, Google ScholarN. S. Meraet al., Engineering Analysis with Boundary Elements 25, 115 (2001). Crossref, Google Scholar E. Divo and A. J. Kasab , Boundary Integral Method for Anisotropic Heat Conduction ( WIT Press , Southampton, United Kingdom , 2001 ) . Google ScholarN. S. Meraet al., Engineering Analysis with Boundary Elements 26, 157 (2002). Crossref, Google Scholar F. Williams , Combustion Theory ( Addison–Wesley Publishing Company , New York , 1985 ) . Google ScholarJ. R. L. Skarda, D. Jacqmin and F. E. McCaughan, J. Fluid Mechanics 366, 109 (1998). Crossref, Google ScholarL. P. Benano–Mellyet al., Int. J. Heat Mass Transfer 44, 1285 (2001). Crossref, Google ScholarR. M. Beam and R. F. Warming, AIAA J. 16, 393 (1978). Crossref, Google ScholarW. R. Briley and H. McDonald, J. Comput. Phys. 34, 54 (1980). Crossref, Google ScholarW. R. Briley and H. McDonald, Computers & Fluids 30, 807 (2001). Crossref, Google ScholarE. Steinthorssonet al., AIAA J. 29, 1101 (1991). Crossref, Google ScholarJ. I. Ramos, Appl. Math. Comput. 100, 201 (1999). Crossref, Google ScholarE. Steinthorsson and T. I–P. Shih, SIAM J. Sci. Comput. 14, 1214 (1993). Crossref, Google ScholarR. W. MacCormack, Computers & Fluids 30, 917 (2001). Crossref, Google Scholar FiguresReferencesRelatedDetailsCited By 1Numerical study of the thermal degradation of isotropic and anisotropic polymeric materialsE. Soler and J.I. Ramos1 Aug 2005 | International Journal of Thermal Sciences, Vol. 44, No. 8 Recommended Vol. 05, No. 03 Metrics History KeywordsAnisotropic mediareaction–diffusion equationslinearization methodsapproximate factorizationPDF download