Meshless solution of two-dimensional incompressible flow problems using the radial basis integral equation method

The two-dimensional incompressible fluid flow problems governed by the velocity–vorticity formulation of the Navier–Stokes equations were solved using the radial basis integral (RBIE) equation method. The RBIE is a meshless method based on the multi-domain boundary element method with overlapping su...

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Bibliographic Details
Published in:Applied mathematical modelling 2013-11, Vol.37 (20-21), p.8985-8998
Main Authors: Ooi, Ean Hin, Popov, Viktor
Format: Article
Language:English
Subjects:
Accuracy
Computational fluid dynamics
Finite element method
Mathematical analysis
Mathematical models
Meshless method
Meshless methods
Navier-Stokes equations
Radial basis functions
Subdomain approach
Two dimensional
Velocity–vorticity formulation
Vorticity
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Summary:The two-dimensional incompressible fluid flow problems governed by the velocity–vorticity formulation of the Navier–Stokes equations were solved using the radial basis integral (RBIE) equation method. The RBIE is a meshless method based on the multi-domain boundary element method with overlapping subdomains. It solves at each node for the potential and its spatial derivatives. This feature of the RBIE is advantageous in solving the velocity–vorticity formulation of the Navier–Stokes equations since the calculated velocity gradients can be used to compute the vorticity that is prescribed as a boundary condition to the vorticity transport equation. The accuracy of the numerical solution was examined by solving the test problem with known analytical solution. Two benchmark problems, i.e. the lid driven cavity flow and the thermally driven cavity flow were also solved. The numerical results obtained using the RBIE showed very good agreement with the benchmark solutions.
ISSN:0307-904X
DOI:10.1016/j.apm.2013.04.035