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Error estimate and adaptive refinement for incompressible Navier‐Stokes equations using the discrete least squares meshless method
Author(s) -
Firoozjaee A.R.,
Afshar Mohammad Hadi
Publication year - 2011
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.2679
Subject(s) - mathematics , node (physics) , navier–stokes equations , boundary value problem , compressibility , residual , boundary (topology) , mathematical optimization , steady state (chemistry) , mathematical analysis , algorithm , mechanics , chemistry , physics , structural engineering , engineering
SUMMARY In this paper, an adaptive refinement strategy based on a node‐moving technique is proposed and used for the efficient solution of the steady‐state incompressible Navier–Stokes equations. The value of a least squares functional of the residual of the governing differential equation and its boundary conditions at nodal points is regarded as a measure of error and used to predict the areas of poor solutions. A node‐moving technique is then used to move the nodal points to the zones of higher numerical errors. The problem is then resolved on the refined distribution of nodes for higher accuracy. A spring analogy is used for the node‐moving methodology in which nodal points are connected to their neighbors by virtual springs. The stiffness of each spring is assumed to be proportional to the errors of its two end points and its initial length. The new positions of the nodal points are found such that the spring system attains its equilibrium state. Some numerical examples are used to illustrate the ability of the proposed scheme for the adaptive solution of the steady‐state incompressible Navier–Stokes equations. The results demonstrate a considerable improvement of the results with a reasonable computational effort by using the proposed adaptive strategy. Copyright © 2011 John Wiley & Sons, Ltd.