Meshless Solution Of 2D And 3D Stokes Flow
Using The Radial Basis Integral Equation Method
Author(s)
E. H. Ooi & V. Popov
Abstract
The calculation of boundary vorticity, which requires the evaluation of the
spatial derivatives of the velocity vector, remains a critical step when solving the
fluid flow problems in the velocity-vorticity formulation. An accurate estimation
of these quantities is required in order to obtain accurate numerical solution and
convergence of the numerical scheme. The radial basis integral equation (RBIE)
method is a meshless method that solves for each node the unknown potential
and its spatial gradients. This unique feature of the RBIE makes it an efficient
numerical tool for solving the fluid flow problems in the velocity-vorticity
formulation, since the velocity derivatives are directly obtained from the system
of equations. In this study, the efficiency of the RBIE for solving the Stokes flow
problems in 2D and 3D is investigated. The accuracy of the numerical results
was assessed by comparing it with the solutions obtained using the finite element
method. Numerical results showed that the RBIE can be used to efficiently and
accurately solve Stokes flow problems.
Keywords: meshless methods, viscous flow, velocity-vorticity formulation, RBIE,
dual reciprocity method.
1 Introduction
One of the most important steps when solving Stokes flow problems in the
velocity-vorticity formulation is the calculation of the boundary vorticity to be
used as boundary conditions in the vorticity transport equation. An accurate
estimation of the boundary vorticity not only yields an accurate numerical
solution but guarantees convergence in the numerical scheme. The vorticity of a
given velocity field is defined by the curl of the velocity vector. Consequently,
Keywords
meshless methods, viscous flow, velocity-vorticity formulation, RBIE,
dual reciprocity method.
Related Book
Other papers in this volume
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