A local-analytic-based discretization procedure for the numerical solution of incompressible flows

We present a local-analytic-based discretization procedure for the numerical solution of viscous fluid flows governed by the incompressible Navier-Stokes equations. The general procedure consists of building local interpolants obtained from local analytic solutions of the linear multi -dimensional advection-diffusion equation, prototypical of the linearized momentum equations. In view of the local analytic behaviour, the resulting computational stencil and coefficient values are functions of the local flow conditions. The velocity-pres sure coupling is achieved by a discrete projection method. Numerical examples in the form of well-established verification and validation benchmarks are presented to demonstrate the capabilities of the formulation. The discretization procedure is implemented alongside the ability to treat embedded and non-matching grids with relative motion. Of interest are flows at high Reynolds number, O(10(5))-O(10(7)), for which the formulation is found to be robust. Applications include flow past a circular cylinder undergoing vortex-induced vibrations (VIV) at high Reynolds number. Copyright (c) 2005 John Wiley & Sons, Ltd.