AD Tools and Prospects for Optimal AD in CFD FluxJacobian Calculations
by
Mohamed Tadjouddine
Cranfield University (RMCS Shrivenham)
Coauthors: Shaun A Forth, John D Pryce

In this paper we consider the problem of linearising the short (O(200) lines of) code that define the numerical fluxes of mass, energy and momentum across a cell face in a finite-volume compressible flow calculation. Typical of such formulations is the numerical flux due to Roe, widely used in the numerical approximation of flow fields containing moderate to strong shocks. Roe's flux take as input 10 variables describing the flow either side of a cell face and returns as output the 5 variables for the numerical flux. We apply four different AD software systems - ADIFOR, ADO1, TAMC and our own Fortran 90 overloaded library. Between them these incorporate the forward and reverse modes, and both operator overloading and source-text translation. For such dense code and small numbers of input and output variables the choice of forward/reverse mode is shown to be implementation dependent, however source-text translation is shown to be consistently superior to overloading. We also discuss the prospects and, in particular, the difficulties in trying to hybridise the forward and reverse modes in such calculations. Applications to 2-D supersonic laminar flows show superiority of a carefully crafted AD Newton solver over a sparse finite differences Newton solver.

http://homepages.feis.herts.ac.uk/~comqun/AD2000/Ext_Abstracts/tadjoudine.ps

Date received: February 11, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cads-67.