Matrix-free second-order methods in implicit time integration for compressible flows using automatic differentiation

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 firstand second-order accurate Jacobian-vector products is compared. It turns out that a hybrid implementation employing both, firstand secondorder accurate methods, significantly reduces the overall execution time of the simulation.