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Comparison of iterative and direct solution methods for viscous flow calculations in body‐fitted co‐ordinates
Author(s) -
Braaten M. E.,
Shyy W.
Publication year - 1986
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.1650060603
Subject(s) - curvilinear coordinates , iterative method , reynolds number , mathematics , skewness , mathematical optimization , cartesian coordinate system , matrix (chemical analysis) , grid , context (archaeology) , algorithm , computer science , geometry , mechanics , turbulence , statistics , physics , materials science , paleontology , composite material , biology
An investigation has been conducted to study the relative performance between the line iterative and direct sparse matrix solution procedures for viscous flow calculations. A key focus point is to assess the method of speeding up the computation in the context of the body‐fitted co‐ordinate system. A series of test problems has been set up to investigate the effects of mesh skewness, Reynolds number and grid size on the two methods. The fully coupled fully implicit treatment of the equations in the direct sparse matrix method leads to rates of convergence that are much more rapid than the iterative method. Whereas the convergence rate of the iterative method is found to decrease monotonically with increasing global mesh skewness and Reynolds number, the direct method is quite insensitive to these parameters. However, the increased complexity of the equations in curvilinear co‐ordinates causes the storage requirements and the cost per iteration of the direct method to be even higher than in corresponding methods using Cartesian co‐ordinates. Consequently, the total CPU time for the direct method is found to be proportional to N 2 (where N is the total number of nodes), which compares unfavourably with the iterative method, where CPU time varies as N . 1,5 Hence, increases in grid size penalize both the CPU time and computer storage requirements of the direct method more severely than the iterative method. These findings make the straightforward adoption of the direct sparse matrix method less attractive in the curvilinear co‐ordinate system. However, the importance of the coupling between the equations on speeding up the convergence of the solution procedure is clearly demonstrated, suggesting possible alternatives for achieving code speed‐up.