Publication: Using Exact Jacobians in an Implicit Newton-Krylov Method
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Using Exact Jacobians in an Implicit Newton-Krylov Method

- Article in a journal -
 

Area
Computational Fluid Dynamics

Author(s)
F. D. Bramkamp , H. M. Bücker , A. Rasch

Published in
Computers & Fluids

Year
2006

Abstract
In an implicit Newton-Krylov method for inviscid, compressible fluid flow, the derivation of the analytic flux Jacobian can become quite complicated depending on the complexity of the numerical flux calculation. Practically, the derivation of the exact Jacobian by hand is an unrealistic option because of the enormous man-hour investment needed. In this work, automatic differentiation is used to evaluate the exact Jacobian of upwind schemes implemented in the flow solver QUADFLOW. We compare the use of exact Jacobians and Jacobians numerically approximated by first-order forward differences. For a two-dimensional airfoil under three different flight conditions (quasi-incompressible flow, compressible subsonic flow, and transonic flow), we show that the robustness and performance of the present finite volume scheme is significantly improved by using exact Jacobians.

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BibTeX
@ARTICLE{
         Bramkamp2006UEJ,
       author = "F. D. Bramkamp and H. M. B{\"u}cker and A. Rasch",
       title = "Using Exact Jacobians in an Implicit Newton-Krylov Method",
       journal = "Computers \& Fluids",
       volume = "35",
       number = "10",
       pages = "1063--1073",
       doi = "10.1016/j.compfluid.2005.10.003",
       abstract = "In an implicit Newton-Krylov method for inviscid, compressible fluid flow, the
         derivation of the analytic flux Jacobian can become quite complicated depending on the complexity of
         the numerical flux calculation. Practically, the derivation of the exact Jacobian by hand is an
         unrealistic option because of the enormous man-hour investment needed. In this work, automatic
         differentiation is used to evaluate the exact Jacobian of upwind schemes implemented in the flow
         solver QUADFLOW. We compare the use of exact Jacobians and Jacobians numerically approximated by
         first-order forward differences. For a two-dimensional airfoil under three different flight
         conditions (quasi-incompressible flow, compressible subsonic flow, and transonic flow), we show that
         the robustness and performance of the present finite volume scheme is significantly improved by
         using exact Jacobians.",
       year = "2006",
       ad_area = "Computational Fluid Dynamics",
       ad_tools = "ADIFOR"
}


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