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An efficient algorithm based on the differential quadrature method for solving Navier–Stokes equations
Author(s) -
Hamed Meraji S.,
Ghaheri Abbas,
Malekzadeh Parviz
Publication year - 2012
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.3665
Subject(s) - quadrature (astronomy) , navier–stokes equations , mathematics , computational fluid dynamics , relaxation (psychology) , nyström method , benchmark (surveying) , boundary value problem , differential equation , numerical partial differential equations , computer science , algorithm , mathematical optimization , mathematical analysis , compressibility , psychology , social psychology , physics , geodesy , aerospace engineering , mechanics , geography , electrical engineering , engineering
SUMMARY In this paper, an approach to improve the application of the differential quadrature method for the solution of Navier–Stokes equations is presented. In using the conventional differential quadrature method for solving Navier–Stokes equations, difficulties such as boundary conditions' implementation, generation of an ill conditioned set of linear equations, large memory storage requirement to store data, and matrix coefficients, are usually encountered. Also, the solution of the generated set of equations takes a long running time and needs high computational efforts. An approach based on the point pressure–velocity iteration method, which is a variant of the Newton–Raphson relaxation technique, is presented to overcome these problems without losing accuracy. To verify its performance, four cases of two‐dimensional flows in single and staggered double lid‐driven cavity and flows past backward facing step and square cylinder, which have been often solved by researchers as benchmark solution, are simulated for different Reynolds numbers. The results are compared with existing solutions in the open literature. Very good agreement with low computational efforts of the approach is shown. It has been concluded that the method can be applied easily and is very time efficient. Copyright © 2012 John Wiley & Sons, Ltd.