Mohamed Tadjouddine, Shaun A Forth & Ning Qin
Published in
International Journal for Numerical Methods in Fluids , Volume 47 ,
Issue 10-11 (January 2005) pp 1315 - 1321. Special
Issue: 8th ICFD Conference on Numerical Methods for Fluid Dynamics
. Issue Edited by Mike J. Baines, Mike J.P. Cullen, Chris Farmer, Mike B.
Giles, M. Rabbitt.
Presented at
The ICFD Conference for Numerical Methods in Fluid Dynamics, Oxford, 29th
March-1st April 2004
Abstract
In CFD, Newton solvers have the attractive property of quadratic
convergence but they require derivative information. An efficient way of
computing derivatives is by algorithmic differentiation (AD) also known
as automatic differentiation or computational differentiation. AD
allows us to evaluate derivatives, usually at a cheap cost, without the
truncation errors associated with finite-differencing. Recently, efficient and
reliable AD tools for evaluating derivatives have been published. In this
paper, we use some of the best AD tools currently available to build up the
system Jacobian involved in the solution of a finite-volume parabolized
Navier-Stokes (PNS) solver. Our aim is to direct scientists and engineers
confronted with the calculation of derivatives to the use of AD and to
highlight those AD tools that they should try. Moreover, we introduce an AD
tool that produces Jacobian code that runs usually twice as fast as that from
conventional AD tools. We further show that the use of AD increases the
performance of a Newton-like solver for the PNS equations.
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Journal Web Entry: http://www3.interscience.wiley.com/cgi-bin/abstract/109880310/ABSTRACT