Adaptive time step control for the incompressible Navier-Stokes equations

作者：John Volker^*; Rang Joachim

来源：Computer Methods in Applied Mechanics and Engineering, 2010, 199(9-12): 514-524.

DOI：10.1016/j.cma.2009.10.005

• Incompressible Navier-Stokes equations
• Implicit theta-schemes
• DIRK methods
• ROW methods
• Adaptive time step control

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 Rosen brock-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.

• 出版日期2010