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Segregated finite element algorithms for the numerical solution of large‐scale incompressible flow problems
Author(s) -
Haroutunian Vahé,
Engelman Michael S.,
Hasbani Isaac
Publication year - 1993
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/fld.1650170405
Subject(s) - conjugate gradient method , finite element method , algorithm , computer science , gaussian elimination , mathematical optimization , scale (ratio) , flow (mathematics) , mathematics , incompressible flow , gaussian , geometry , physics , quantum mechanics , thermodynamics
Abstract This paper presents results of an ongoing research program directed towards developing fast and efficient finite element solution algorithms for the simulation of large‐scale flow problems. Two main steps were taken towards achieving this goal. The first step was to employ segregated solution schemes as opposed to the fully coupled solution approach traditionally used in many finite element solution algorithms. The second step was to replace the direct Gaussian elimination linear equation solvers used in the first step with iterative solvers of the conjugate gradient and conjugate residual type. The three segregated solution algorithms developed in step one are first presented and their integrity and relative performance demonstrated by way of a few examples. Next, the four types of iterative solvers (i.e. two options for solving the symmetric pressure type equations and two options for solving the non‐symmetric advection–diffusion type equations resulting from the segregated algorithms) together with the two preconditioning strategies employed in our study are presented. Finally, using examples of practical relevance the paper documents the large gains which result in computational efficiency, over fully coupled solution algorithms, as each of the above two main steps are introduced. It is shown that these gains become increasingly more dramatic as the complexity and size of the problem is increased.