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A compact RBF-FD based meshless method for the incompressible Navier–Stokes equations

A compact RBF-FD based meshless method for the incompressible Navier–Stokes equations
A compact RBF-FD based meshless method for the incompressible Navier–Stokes equations
Meshless methods for solving fluid and fluid-structure problems have become a promising alternative to the finite volume and finite element methods. In this paper, a mesh-free computational method based on radial basis functions in a finite difference mode (RBF-FD) has been developed for the incompressible Navier—Stokes (NS) equations in stream function vorticity form. This compact RBF-FD formulation generates sparse coefficient matrices, and hence advancing solutions will in time be of comparatively lower cost. The spatial discretization of the incompressible NS equations is done using the RBF-FD method and the temporal discretization is achieved by explicit Euler time-stepping and the Crank—Nicholson method. A novel ghost node strategy is used to incorporate the no-slip boundary conditions. The performance of the RBF-FD scheme with the ghost node strategy is validated against a variety of benchmark problems, including a model fluid—structure interaction problem, and is found to be in a good agreement with the existing results. In addition, a higher-order RBF-FD scheme (which uses ideas from Hermite interpolation) is then proposed for solving the NS equations.
meshless method, radial basis functions, finite difference, incompressible navier–stokes equations, fluid–structure interaction, stream function
1475-0902
275-290
Chinchapatnam, P.P.
61221cab-afae-46d5-a6ea-14eb472d5522
Djidjeli, K.
94ac4002-4170-495b-a443-74fde3b92998
Nair, P.B.
d4d61705-bc97-478e-9e11-bcef6683afe7
Tan, M.
4d02e6ad-7915-491c-99cc-a1c85348267c
Chinchapatnam, P.P.
61221cab-afae-46d5-a6ea-14eb472d5522
Djidjeli, K.
94ac4002-4170-495b-a443-74fde3b92998
Nair, P.B.
d4d61705-bc97-478e-9e11-bcef6683afe7
Tan, M.
4d02e6ad-7915-491c-99cc-a1c85348267c

Chinchapatnam, P.P., Djidjeli, K., Nair, P.B. and Tan, M. (2009) A compact RBF-FD based meshless method for the incompressible Navier–Stokes equations. Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment, 233 (3), 275-290. (doi:10.1243/14750902JEME151).

Record type: Article

Abstract

Meshless methods for solving fluid and fluid-structure problems have become a promising alternative to the finite volume and finite element methods. In this paper, a mesh-free computational method based on radial basis functions in a finite difference mode (RBF-FD) has been developed for the incompressible Navier—Stokes (NS) equations in stream function vorticity form. This compact RBF-FD formulation generates sparse coefficient matrices, and hence advancing solutions will in time be of comparatively lower cost. The spatial discretization of the incompressible NS equations is done using the RBF-FD method and the temporal discretization is achieved by explicit Euler time-stepping and the Crank—Nicholson method. A novel ghost node strategy is used to incorporate the no-slip boundary conditions. The performance of the RBF-FD scheme with the ghost node strategy is validated against a variety of benchmark problems, including a model fluid—structure interaction problem, and is found to be in a good agreement with the existing results. In addition, a higher-order RBF-FD scheme (which uses ideas from Hermite interpolation) is then proposed for solving the NS equations.

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Published date: 1 September 2009
Keywords: meshless method, radial basis functions, finite difference, incompressible navier–stokes equations, fluid–structure interaction, stream function
Organisations: Computational Engineering and Design, Fluid Structure Interactions Group

Identifiers

Local EPrints ID: 69138
URI: https://eprints.soton.ac.uk/id/eprint/69138
ISSN: 1475-0902
PURE UUID: f02f6025-0a36-4442-92ec-1d5ddec5dbdd

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Date deposited: 21 Oct 2009
Last modified: 19 Jul 2017 00:13

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Contributors

Author: P.P. Chinchapatnam
Author: K. Djidjeli
Author: P.B. Nair
Author: M. Tan

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