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A comparative study of fractional step method in its quasi-implicit, semi-implicit and fully-explicit forms for incompressible flows
International Journal of Numerical Methods for Heat & Fluid Flow, Volume: 26, Issue: 3/4, Pages: 595 - 623
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DOI (Published version): 10.1108/HFF-06-2015-0233
The present review describes and analyses a class of finite element fractional step methodsfor solving the incompressible Navier-Stokes equations. Our objective is not to reproduce the extensivecontributions on the subject, but to report on our long-term experience with and provide a unified overvie...
|Published in:||International Journal of Numerical Methods for Heat & Fluid Flow|
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The present review describes and analyses a class of finite element fractional step methodsfor solving the incompressible Navier-Stokes equations. Our objective is not to reproduce the extensivecontributions on the subject, but to report on our long-term experience with and provide a unified overviewof a particular approach: the characteristic based split method. Three procedures, the semi-implicit, quasi-implicit and fully-explicit, are studied and compared. This work provides a thorough assessment of theaccuracy and efficiency of these schemes, both for a first and second order pressure split. In transientproblems, the quasi-implicit form significantly outperforms the fully-explicit approach. The second order(pressure) fractional step method displays significant convergence and accuracy benefits when the quasi-implicit projection method is employed. The fully-explicit method, utilising artificial compressibility and apseudo time stepping procedure, requires no second order fractional split to achieve second order or higheraccuracy. While the fully-explicit form is efficient for steady state problems, due to its ability to handle localtime stepping, the quasi-implicit is the best choice for transient flow calculations with time independent boundary conditions. The semi-implicit form, with its stability restrictions, is the least favoured of all the three forms for incompressible flow calculations.
Faculty of Science and Engineering