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Adaptive time step control for the incompressible Navier-Stokes equations. (English) Zbl 1227.76048
Summary: Adaptive time stepping is an important tool in Computational Fluid Dynamics for controlling the accuracy of simulations and for enhancing their efficiency. This paper presents a systematic study of three classes of implicit and linearly implicit time stepping schemes with adaptive time step control applied to a 2D laminar flow around a cylinder: \(\theta\)-schemes, diagonal-implicit Runge-Kutta (DIRK) methods and Rosenbrock-Wanner (ROW) methods. The time step is controlled using embedded methods. It is shown that several ROW methods clearly outperform the more standard \(\theta\)-schemes and the DIRK methods. The results depend on a prescribed tolerance in the time step control algorithm, whose appropriate choice varies from scheme to scheme.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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