288 IGPM288.pdf        October 2008
TITLE Matrix-Free Second-Order Methods in Implicit Time Integration for Compressible Flows Using Automatic Differentiation
AUTHORS Frank Dieter Bramkamp, Bernhard Pollul, Arno Rasch, Gero Schieffer
ABSTRACT In the numerical simulation of inviscid and viscous compressible fluid flow, implicit Newton-Krylov methods are frequently used. A crucial ingredient of Krylov subspace methods is the evaluation of the product of the Jacobian matrix of the spatial operator, e.g., fluxes, and a Krylov vector. In this article we consider a matrix-free implementation of the Jacobian-vector product within the flow solver QUADFLOW using automatic differentiation. The convergence of the nonlinear iteration using first- and second-order accurate Jacobian-vector products is compared. It turns out that a hybrid implementation employing both, first- and second- order accurate methods, significantly reduces the overall execution time of the simulation.
KEYWORDS Matrix-free methods, Newton-Krylov, Automatic differentiation, QUADFLOW, ADIFOR