

AD Tools and Prospects for Optimal AD in CFD Flux Jacobian Calculations
incollection
  

Area Computational Fluid Dynamics 
Author(s)
Mohamed Tadjouddine
, Shaun A. Forth
, John D. Pryce

Published in Automatic Differentiation of Algorithms: From Simulation to Optimization

Editor(s) George Corliss, Christèle Faure, Andreas Griewank, Laurent Hascoët, Uwe Naumann 
Year 2002 
Publisher Springer 
Abstract We consider the problem of linearising the short (approximately 100 lines of) code that defines 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 takes 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 present results concerning the efficiency of derivative calculations for Roe's flux using several currently available ad tools. We also present preliminary work on deriving near optimal differentiated code using the node elimination approach. We show that such techniques, within a source transformation approach, will yield substantial gains for application code such as the Roe flux. 
CrossReferences Corliss2002ADo 
AD Tools AD01, ADIFOR, TAMC 
BibTeX
@INCOLLECTION{
Tadjouddine2002ATa,
author = "Mohamed Tadjouddine and Shaun A. Forth and John D. Pryce",
editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent
Hasco{\"e}t and Uwe Naumann",
year = "2002",
title = "{AD} Tools and Prospects for Optimal {AD} in {CFD} Flux {J}acobian Calculations",
booktitle = "Automatic Differentiation of Algorithms: From Simulation to Optimization",
series = "Computer and Information Science",
pages = "255261",
publisher = "Springer",
address = "New York, NY",
abstract = "We consider the problem of linearising the short (approximately $100$ lines of)
code that defines 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 takes 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 present results concerning the
efficiency of derivative calculations for Roe's flux using several currently available AD
tools. We also present preliminary work on deriving near optimal differentiated code using the node
elimination approach. We show that such techniques, within a source transformation approach, will
yield substantial gains for application code such as the Roe flux.",
ad_tools = "AD01, ADIFOR, TAMC",
ad_area = "Computational Fluid Dynamics",
chapter = "30",
pdf = "http://www.rmcs.cranfield.ac.uk/departments/esd/amorg/research/mtsaf_ad2000.pdf",
ps = "http://www.rmcs.cranfield.ac.uk/departments/esd/amorg/research/mtsaf_ad2000.ps.gz",
url = "http://www.rmcs.cranfield.ac.uk/departments/esd/amorg/research/mtsaf_ad2000.html",
crossref = "Corliss2002ADo"
}
 
back

