Publication: AD Tools and Prospects for Optimal AD in CFD Flux Jacobian Calculations
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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.

Cross-References
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 = "255--261",
       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"
}


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