Resolving non‐symmetry in flows via subdomain shifts

References

• Babinsky , H. 1999 . Aerodynamic improvements of paraglider performance . Aeronautical Journal, , 103 (1027) : 421 – 428 .
   Web of Science ®Google Scholar
• Barrett , R. , Berry , M. , Chan , T.F , Demmel , J. , Donato , J. , Dongarra , J. , Ei‐jkhout , V. , Pozo , R. , Romine , C. and Van der Vorst , H. 1994 . Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. , Philadelphia : SIAM .
   Google Scholar
• Bjorstad , P.E. and Widlund , O.B. 1986 . Iterative methods for the solution of elliptic problems on regions partitioned into substructures . SIAM Journal on Scientific Computing, , 23 : 1097 – 1120 . Available from Internet: http://www.jstor.org/stable/2157416
   Google Scholar
• Brown , P.N. and Saad , Y. 1990 . Hybrid Krylov methods for nonlinear‐systems of equations . SIAM Journal on Scientific and Statistical Computing , ll (3) : 450 – 481 . Doi:10.1137/0911026
   Google Scholar
• Cai , X.C. and Keyes , D.E. 2002 . Nonlinearly preconditioned inexact Newton algorithms . SIAM Journal on Scientific Computing, , 24 (1) : 183 – 200 . Doi:10.1137/S106482750037620X.
   Web of Science ®Google Scholar
• Cai , X.C. , Keyes , D.E. and Marcinkowski , L. 2002 . Non‐linear additive Schwarz precon‐ditioners and application in computational fluid dynamics . International Journal for Numerical Methods in Fluids, , 40 (12) : 1463 – 1470 . Doi:10.1002/fld.404.
   Web of Science ®Google Scholar
• Chorin , A.J. 1967 . A numerical method for solving incompressible viscous flow problems . Journal of Computational Physics , 2 (l) : 12 – 26 . Doi:10.1016/0021–9991(67)90037‐X.
   Google Scholar
• Čiegis , R. , Iliev , O. and Lakdawala , Z. 2007 . On parallel numerical algoritms for simulating industrial filtration problems . Computational Methods in Applied Mathematics, , 7 (2) : 118 – 134 .
   Google Scholar
• Čiegis , Raim. , Čiegis , Rem. and Meilūnas , M. 2008 . Parallel numerical for optimization of electrical cables . Math. Model. Anal, , 13 (4) : 471 – 482 .
   Web of Science ®Google Scholar
• Escudier , M.R , Gouldson , I.W. , Oliveira , RJ. and Pinho , F.T. 2000 . Effect of inner cylinder rotation on laminar flow of a Newtonian fluid through an eccentric annulus . International Journal of Heat and Fluid Flow , 21 (l) : 92 – 103 . Doi:10.1016/S0142–727X(99)00059–4.
   Google Scholar
• Felippa , C.A. , Park , K.C. and Farhat , C. 2001 . Partitioned analysis of coupled mechanical systems . Computer Methods in Applied Mechanics and Engineering, , 190 (24–25) : 3247 – 3270 . Doi:10.1016/S0045–7825(00)00391–1.
   Web of Science ®Google Scholar
• Houzeaux , G. and Codina , R. 2003 . A Chimera method based on a Dirich‐let/Neumann (Robin) coupling for the NavierU‐Stokes equations . Computer‐Methods in Applied Mechanics and Engineering, , 192 (31–32) : 3343 – 3377 . Doi:10.1016/S0045–7825(03)00276–7.
   Web of Science ®Google Scholar
• Incropera , F.P. and DeWitt , D.P. 2001 . Introduction to Heat Transfer. , New York : Wiley .
   Google Scholar
• Jameson , A. and Yoon , S. 1987 . Lower‐upper implicit schemes with multiple grids for the Euler equations . AIAA Journal, , 25 (7) : 929 – 935 .
   Web of Science ®Google Scholar
• Karypis , G. and Kumar , V. 1998 . A fast and high quality multilevel scheme for partitioning irregular graphs . SIAM Journal on Scientific Computing , 20 (l) : 359 – 392 . Doi:10.1137/S1064827595287997
   Google Scholar
• Kron , G. 1953 . A set of principles to interconnect the solutions of physical systems . Journal of Applied Physics, , 24 (8) : 965 – 980 . Doi:10.1063/1.1721447
   Web of Science ®Google Scholar
• Landmann , B. and Montagnac , M. 2010 . A highly automated parallel Chimera method for overset grids based on the implicit hole cutting technique . International Journal for Numerical Methods in Fluids , Doi:10.1002/fld.2292
   Web of Science ®Google Scholar
• Mathew , T. 2008 . Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations. , Berlin : Springer .
   Google Scholar
• Patankar , S.V. 1980 . Numerical Heat Transfer and Fluid Flow. , Washington : Hemisphere Publishing .
   Google Scholar
• Przemieniecki , J.S. 1963 . Matrix structural analysis of substructures . AIAA Journal, , 1 (1) : 138 – 147 .
   Web of Science ®Google Scholar
• Qini , N. , Ludlow , D.K. and Shaw , S.T. 2000 . A matrix‐free preconditioned Newton‐GMRES method for unsteady Navier‐UStokes solutions . International Journal for Numerical Methods in Fluids, , 33 (2) : 223 – 248 . Doi:10.1002/(SICI)1097–0363(20000530)33:2<223::AID‐FLD10>3.0.CO;2‐V.
   Web of Science ®Google Scholar
• Quarteroni , A. and Valli , A. 1999 . Domain Decomposition Methods for Partial Differential Equations. , Oxford : Oxford University Press .
   Google Scholar
• Roache , P.J. 1998 . Fundamentals of computational fluid dynamics. , Albuquerque : Hermosa Publishers .
   Google Scholar
• Saad , Y. and Schultz , M. 1986 . A generalized minimal residual algorithm for solving nonsymmetric linear systems . SIAM Journal on Scientific and Statistical Computing, , 7 (3) : 856 – 869 . Doi:10.1137/0907058
   Web of Science ®Google Scholar
• Schwarz , H.A. 1870 . Über einen Grenzübergang durch alternierendes Verfahren . Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich, , 15 : 272 – 286 .
   Google Scholar
• Smith , B. , Bjorstad , P. and Gropp , W. 1996 . Domain Decomposition. , Philadelphia : Cambridge Publications .
   Google Scholar
• Toselli , A. and Widlund , O. 2004 . Domain Decomposition Methods ‐ Algorithms and Theory. , Berlin : Springer .
   Google Scholar
• Wall , W. , Gamnitzer , P. and Gerstenberger , A. 2008 . Fluid‐structure interaction approaches on fixed grids based on two different domain decomposition ideas . International Journal of Computational Fluid Dynamics, , 22 : 411 – 427 . Doi:10.1080/10618560802208567
   Web of Science ®Google Scholar
• Wohlmuth , B.I. and Valli , A. 2001 . Discretization Methods and Iterative Solvers Based on Domain Decomposition. , Berlin : Springer .
   Google Scholar
• Yang , M. and Du , Q. 2004 . A Schwarz alternating algorithm for elliptic boundary value problems in an infinite domain with a concave angle . Applied Mathematics and Computation, , 159 : 199 – 220 . Doi:10.1016/j.amc.2003.10.042.
   Web of Science ®Google Scholar
• This work was funded by a grant from Bogazici University Research Fund, BAP N 07A601D.
   Google Scholar