Physics-informed neural networks (PINNs) are successful machine-learning methods for the solution and identification of partial differential equations. We employ PINNs solving Reynolds-averaged Navier–Stokes equations incompressible turbulent flows without any specific model or assumption turbulence by taking only data on domain boundaries. first show applicability laminar Falkner–Skan boundary...

We propose an iterative method for solving the Falkner-Skan equation. The method provides approximate analytical solutions which consist of coefficients of the previous iterate solution. By some examples, we show that the presented method with a small number of iterations is competitive with the existing method such as Adomian decomposition method. Furthermore, to improve the accuracy of the pr...

A numerical technique is presented for the solution of Falkner-Skan equation. The nonlinear ordinary differential equation is solved using Chebyshev cardinal functions. The method have been derived by first truncating the semi-infinite physical domain of the problem to a finite domain and expanding the required approximate solution as the elements of Chebyshev cardinal functions. Using the oper...

* Correspondence: stanford. [email protected] Department of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa Full list of author information is available at the end of the article Abstract This article presents an improved spectral-homotopy analysis method (ISHAM) for solving nonlinear differential equations. The implementation of this new technique is show...

The boundary layers of rainbow trout, Oncorhynchus mykiss [0.231±0.016 m total body length (L) (mean±s.d.); N=6], swimming at 1.6±0.09 L s-1 (N=6) in an experimental flow channel (Reynolds number, Re=4×105) with medium turbulence (5.6% intensity) were examined using the particle image velocimetry technique. The tangential flow velocity distributions in the pectoral and pelvic surface regions (a...