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This paper is concerned with the development and testing of advancedtime-stepping methods suited for the integration of time-accurate, real-worldapplications of computational fluid dynamics (CFD). The performance of severaltime discretization methods is studied numerically with regards tocomputational efficiency, order of accuracy, and stability, as well as theability to treat effectively stiff problems. We consider matrix-freeimplementations, a popular approach for time-stepping methods applied to largeCFD applications due to its adherence to scalable matrix-vector operations anda small memory footprint. We compare explicit methods with matrix-freeimplementations of implicit, linearly-implicit, as well as Rosenbrock-Krylovmethods. We show that Rosenbrock-Krylov methods are competitive with existingtechniques excelling for a number of problem types and settings.

A Numerical Investigation of Matrix-Free Implicit Time-Stepping Methods for Large CFD Simulations