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A stabilized RBF finite difference method for convection dominated flows over meshfree nodes

A stabilized RBF finite difference method for convection dominated flows over meshfree nodes
A stabilized RBF finite difference method for convection dominated flows over meshfree nodes

In this paper, a stabilized solution scheme is presented for solving highly convective flow equations on meshfree nodal distribution. The stabilized terms are obtained by considering higher order approximation of governing differential equations over finite control volume while applying force and momentum balance. Spatial derivatives, of resulting flow equations, are treated with Radial Basis Functions in Finite Difference Method (RBF-FD) over meshfree domain. The characteristic length, for applying equilibrium of forces and momentum, is proposed to be a function of Reynolds number and flow velocity. Performance and accuracy of the proposed scheme is tested for 1-D Convection-Diffusion equations. Numerical tests are conducted for initial conditions having stepped as well as uniformly varying field variables. The scheme is found to be effective in suppressing the non-physical numerical fluctuations associated with convection dominated flows. Accuracy of the solution with stabilized term is found to be higher than the one without stabilization. The solution scheme is also used for flow around static NACA0012 airfoil at Reynolds Number 5000, 10000 and 50000. The stabilization term is found to effectively suppress the numerical oscillation when compared to non-stabilized scheme.

American Institute of Aeronautics and Astronautics
Javed, A.
88cda024-ba02-4a2e-9bf8-90b0d201f81b
Djidjeli, K.
94ac4002-4170-495b-a443-74fde3b92998
Jamil, M.
ffcef682-9ea2-41a9-bcbc-993f0f129004
Arif, I.
17468584-9a15-4da7-a579-a6be46cc5459
Javed, A.
88cda024-ba02-4a2e-9bf8-90b0d201f81b
Djidjeli, K.
94ac4002-4170-495b-a443-74fde3b92998
Jamil, M.
ffcef682-9ea2-41a9-bcbc-993f0f129004
Arif, I.
17468584-9a15-4da7-a579-a6be46cc5459

Javed, A., Djidjeli, K., Jamil, M. and Arif, I. (2018) A stabilized RBF finite difference method for convection dominated flows over meshfree nodes. In AIAA Aerospace Sciences Meeting. American Institute of Aeronautics and Astronautics.. (doi:10.2514/6.2018-1565).

Record type: Conference or Workshop Item (Paper)

Abstract

In this paper, a stabilized solution scheme is presented for solving highly convective flow equations on meshfree nodal distribution. The stabilized terms are obtained by considering higher order approximation of governing differential equations over finite control volume while applying force and momentum balance. Spatial derivatives, of resulting flow equations, are treated with Radial Basis Functions in Finite Difference Method (RBF-FD) over meshfree domain. The characteristic length, for applying equilibrium of forces and momentum, is proposed to be a function of Reynolds number and flow velocity. Performance and accuracy of the proposed scheme is tested for 1-D Convection-Diffusion equations. Numerical tests are conducted for initial conditions having stepped as well as uniformly varying field variables. The scheme is found to be effective in suppressing the non-physical numerical fluctuations associated with convection dominated flows. Accuracy of the solution with stabilized term is found to be higher than the one without stabilization. The solution scheme is also used for flow around static NACA0012 airfoil at Reynolds Number 5000, 10000 and 50000. The stabilization term is found to effectively suppress the numerical oscillation when compared to non-stabilized scheme.

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More information

e-pub ahead of print date: 7 January 2018
Published date: 8 January 2018
Venue - Dates: AIAA Aerospace Sciences Meeting, 2018, Kissimmee, United States, 2018-01-08 - 2018-01-12

Identifiers

Local EPrints ID: 419417
URI: http://eprints.soton.ac.uk/id/eprint/419417
PURE UUID: 6df2dc86-4494-4094-83fe-5523da4ec096

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Date deposited: 12 Apr 2018 16:30
Last modified: 09 Jan 2019 17:32

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Contributors

Author: A. Javed
Author: K. Djidjeli
Author: M. Jamil
Author: I. Arif

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