A Self-Adaptive Strategy for the Time Integration of Navier-Stokes Equations

Abstract

An efficient self-adaptive strategy for the explicit time integration of Navier-Stokes equations is presented. Unlike the conventional explicit integration schemes, it is not based on a standard CFL condition. Instead, the eigenvalues of the dynamical system are analytically bounded and the linear stability domain of the time-integration scheme is adapted in order to maximize the time step. The method works independently of the underlying spatial mesh; therefore, it can be easily integrated into structured or unstructured codes. The additional computational cost is minimal, and a significant increase of the time step is achieved without losing accuracy. The effectiveness and robustness of the method are demonstrated on both a Cartesian staggered and an unstructured collocated formulation. In practice, CPU cost reductions up to more than 4 with respect to the conventional approach have been measured.

Acknowledgments

This work has been financially supported by the Ministerio de Ciencia e Innovación, Spain; Contract/grant numbers ENE2010-17801, the Collaboration Project between the Universitat Politècnica de Catalunya and Termo Fluids S.L (ref. C06650), and a Juan de la Cierva postdoctoral contract (JCI-2009-04910) of the Ministerio de Ciencia e Innovación. Structured mesh simulations have been carried out on the IBM MareNostrum supercomputer at the Barcelona Supercomputing Center. The authors gratefully acknowledge these institutions.