Time Integration Schemes for the Unsteady Navier-Stokes Equations
نویسندگان
چکیده
The e ciency and accuracy of several time integration schemes are investigated for the unsteady Navier-Stokes equations. This study focuses on the e ciency of higher-order Runge-Kutta schemes in comparison with the popular Backward Di erencing Formulations. For this comparison an unsteady two-dimensional laminar ow problem is chosen, i.e. ow around a circular cylinder at Re=1200. It is concluded that for realistic error tolerances (smaller than 10 ) fourthand fth-order Runge Kutta schemes are the most e cient. For reasons of robustness and computer storage, the fourth-order RungeKutta method is recommended. The e ciency of the fourth-order Runge-Kutta scheme exceeds that of second-order Backward Di erence Formula (BDF2) by a factor of 2:5 at engineering error tolerance levels (10 1-10 2). E ciency gains are more dramatic at smaller tolerances.
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