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

Abstract

SUMMARYWe present a local-analytic-based discretization procedure for the numerical solution of viscous uid ows 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 advectiondi usion equation, prototypical of the linearized momentum equations. In view of the local analytic behaviour, the resulting computational stencil and coe cient values are functions of the local ow conditions. The velocity-pressure coupling is achieved by a discrete projection method. Numerical examples in the form of well-established veriÿcation 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 ows at high Reynolds number, O(10 5 ) -O(10 7 ), for which the formulation is found to be robust. Applications include ow past a circular cylinder undergoing vortex-induced vibrations (VIV) at high Reynolds number.

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