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ITERATIVE SOLUTION OF INCOMPRESSIBLE NAVIER–STOKES EQUATIONS ON THE MEIKO COMPUTING SURFACE
Author(s) -
TANYI B. A.,
THATCHER R. W.
Publication year - 1996
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19960229)22:4<225::aid-fld313>3.0.co;2-8
Subject(s) - generalized minimal residual method , linear system , preconditioner , conjugate gradient method , uniprocessor system , mathematics , discretization , iterative method , system of linear equations , relaxation (psychology) , multigrid method , biconjugate gradient stabilized method , solver , gauss–seidel method , linear equation , laminar flow , computer science , mathematical optimization , multiprocessing , parallel computing , mathematical analysis , partial differential equation , physics , mechanics , psychology , social psychology
The numerical discretization of the equations governing fluid flow results in coupled, quasi‐linear and non‐symmetric systems. Various approaches exist for resolving the non‐linearity and couplings. During each non‐linear iteration, nominally linear systems are solved for each of the flow variables. Line relaxation techniques are traditionally employed for solving these systems. However, they could be very expensive for realistic applications and present serious synchronization problems in a distributed memory parallel environment. In this paper the discrete linear systems are solved using the generalized conjugate gradient method of Concus and Golub. The performance of this algorithm is compared with the line Gauss–Seidel algorithm for laminar recirculatory flow in uni‐ and multiprocessor environments. The uniprocessor performances of these algorithms are also compared with that of a popular iterative solver for non‐symmetric systems (the GMRES algorithm).