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Numerical simulations of the steady Navier–Stokes equations using adaptive meshing schemes
Author(s) -
Ju Lili,
Lee HyungChun,
Tian Li
Publication year - 2007
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.1549
Subject(s) - discretization , finite element method , voronoi diagram , delaunay triangulation , mesh generation , mathematics , navier–stokes equations , convergence (economics) , rate of convergence , quadratic equation , polygon mesh , centroidal voronoi tessellation , mathematical optimization , compressibility , algorithm , computer science , mathematical analysis , geometry , mechanics , computer network , channel (broadcasting) , economics , thermodynamics , economic growth , physics
In this paper, we consider an adaptive meshing scheme for solution of the steady incompressible Navier–Stokes equations by finite element discretization. The mesh refinement and optimization are performed based on an algorithm that combines the so‐called conforming centroidal Voronoi Delaunay triangulations (CfCVDTs) and residual‐type local a posteriori error estimators. Numerical experiments in the two‐dimensional space for various examples are presented with quadratic finite elements used for the velocity field and linear finite elements for the pressure. The results show that our meshing scheme can equally distribute the errors over all elements in some optimal way and keep the triangles very well shaped as well at all levels of refinement. In addition, the convergence rates achieved are close to the best obtainable. Extension of this approachto three‐dimensional cases is also discussed and the main challenge is the efficient implementation of three‐dimensional CfCVDT generation that is still under development. Copyright © 2007 John Wiley & Sons, Ltd.