Numerical solution of Navier-Stokes equations using multiquadric radial basis function networks

Mai-Duy, Nam and Tran-Cong, Thanh (2001) Numerical solution of Navier-Stokes equations using multiquadric radial basis function networks. International Journal for Numerical Methods in Fluids, 37 (1). pp. 65-86. ISSN 0271-2091


A numerical method based on radial basis function networks (RBFNs) for solving steady incompressible viscous flow problems (including Boussinesq materials) is presented in this paper. The method uses a 'universal approximator' based on neural network methodology to represent the solutions. The method is easy to implement and does not require any kind of 'finite element-type' discretization of the domain and its boundary. Instead, two sets of random points distributed throughout the domain and on the boundary are required. The first set defines the centres of the RBFNs and the second defines the collocation points. The two sets of points can be different; however, experience shows that if the two sets are the same better results are obtained. In this work the two sets are identical and hence commonly referred to as the set of centres. Planar Poiseuille, driven cavity and natural convection flows are simulated to verify the method. The numerical solutions obtained using only relatively low densities of centres are in good agreement with analytical and benchmark solutions available in the literature. With uniformly distributed centres, the method achieves Reynolds number Re = 100 000 for the Poiseuille flow (assuming that laminar flow can be maintained) using the density of 11x11, Re = 400 for the driven cavity flow with a density of 33x33 and Rayleigh number Ra = 1 000 000 for the natural convection flow with a density of 27x27.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Deposited in accordance with the copyright policy of the publisher.
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 11 Oct 2007 01:14
Last Modified: 02 Jul 2013 22:46
Uncontrolled Keywords: mesh-free method; Navier-Stokes equations; radial basis function networks; streamfunction-vorticity formulation
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
09 Engineering > 0915 Interdisciplinary Engineering > 091501 Computational Fluid Dynamics
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI: 10.1002/fld.165

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