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An implicit meshless method for application in computational fluid dynamics

Authors


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

E-mail: D.Kennett@liverpool.ac.uk

SUMMARY

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.

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