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"
}