In this paper we investigate energy-conserving time integration of the incompressible Navier-Stokes equations by employing linearly implicit Runge-Kutta methods. Such methods have the same order of accuracy and the same stability properties as fully nonlinear methods, but are much cheaper from a computational point of view. Numerical experiments show that if the problem is smooth in time and if second order accuracy is sufficient, the linearly implicit methods can be significantly more efficient at large time steps. However, for less smooth problems and higher order methods, the linearly implicit methods do not have a clear benefit over the nonlinear methods, because the reduction in computational time is generally offset by a larger error constant.
|Titel||ECCOMAS 2012 -European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers|
|Status||Gepubliceerd - 2012|
Sanderse, B., & Koren, B. (2012). Linearly implicit energy-conserving Runge-Kutta methods for the incompressible Navier-Stokes equations. In ECCOMAS 2012 -European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers (blz. 2294-2306)