Research Article

Elimination AD applied to Jacobian assembly for an implicit compressible CFD solver

  1. Mohamed Tadjouddine1,*,
  2. Shaun A. Forth1,
  3. Ning Qin2

Article first published online: 27 JAN 2005

DOI: 10.1002/fld.927

Issue

International Journal for Numerical Methods in Fluids

International Journal for Numerical Methods in Fluids

Special Issue: 8th ICFD Conference on Numerical Methods for Fluid Dynamics

Volume 47, Issue 10-11, pages 1315–1321, 10 - 20 April 2005

Additional Information

How to Cite

Tadjouddine, M., Forth, S. A. and Qin, N. (2005), Elimination AD applied to Jacobian assembly for an implicit compressible CFD solver. International Journal for Numerical Methods in Fluids, 47: 1315–1321. doi: 10.1002/fld.927

Author Information

  1. 1

    Engineering Systems Department, Cranfield University (Shrivenham Campus), ESD AMOR Group, Swindon SN68LA, U.K.

  2. 2

    Department of Mechanical Engineering, The University of Sheffield, Mappin Street, S1 3JD, U.K.

*Engineering Systems Department, Cranfield University (Shrivenham Campus), ESD AMOR Group, Swindon SN68LA, U.K.

Publication History

  1. Issue published online: 9 MAR 2005
  2. Article first published online: 27 JAN 2005
  3. Manuscript Accepted: 7 DEC 2004
  4. Manuscript Revised: 17 SEP 2004
  5. Manuscript Received: 27 APR 2004

Funded by

  • EPSRC. Grant Number: GR/R85358/01

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Keywords:

  • PNS;
  • Newton solver;
  • vertex elimination algorithm;
  • algorithmic differentiation

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. Copyright © 2005 John Wiley & Sons, Ltd.

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