Neural networks for BEM analysis of steady viscous flows

This paper presents a new neural network-boundary integral approach for analysis of steady viscous fluid flows. Indirect radial basis function networks (IRBFNs) which perform better than element-based methods for function interpolation, are introduced into the BEM scheme to represent the variations of velocity and traction along the boundary from the nodal values. In order to assess the effect of IRBFNs, the other features used in the present work remain the same as those used in the standard BEM. For example, Picard-type scheme is utilized in the iterative procedure to deal with the non-linear convective terms while the calculation of volume integrals and velocity gradients are based on the linear finite element-based method. The proposed IRBFN-BEM is verified on the driven cavity viscous flow problem and can achieve a moderate Reynolds number of 1400 using a relatively coarse uniform mesh. The results obtained such as the velocity profiles along the horizontal and vertical centrelines as well as the properties of the primary vortex are in very good agreement with the benchmark solution. Furthermore, the secondary vortices are also captured by the present method. Thus, it appears that an ability to represent the boundary solution accurately can significantly improve the overall solution accuracy of the BEM.