An implicit meshless method for application in computational fluid dynamics


Correspondence to: David Kennett, School of Engineering, University of Liverpool, Liverpool, England L69 3BX, United Kingdom.



An implicit meshless scheme is developed for solving the Euler equations, as well as the laminar and Reynolds-averaged Navier–Stokes equations. Spatial derivatives are approximated using a least squares method on clouds of points. The system of equations is linearised, and solved implicitly using approximate, analytical Jacobian matrices and a preconditioned Krylov subspace iterative method. The details of the spatial discretisation, linear solver and construction of the Jacobian matrix are discussed; and results that demonstrate the performance of the scheme are presented for steady and unsteady two dimensional fluid flows. Copyright © 2012 John Wiley & Sons, Ltd.