Analysis of a Stabilized CNLF Method with Fast Slow Wave Splittings for Flow Problems
Abstract
In this work, we study Crank–Nicolson leap-frog (CNLF) methods with fast-slow wave splittings for Navier–Stokes equations (NSE) with a rotation/Coriolis force term, which is a simplification of geophysical flows. We propose a new stabilized CNLF method where the added stabilization completely removes the method's CFL time step condition. A comprehensive stability and error analysis is given. We also prove that for Oseen equations with the rotation term, the unstable mode (for which u n + 1 + u n - 1 ≡ 0 $u^{n+1}+u^{n-1}\equiv 0 $ ) of CNLF is asymptotically stable. Numerical results are provided to verify the stability and the convergence of the methods.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Apr 02, 2015
- Source ID
- 10.1515/cmam-2015-0010
Entities
People
- Hoang Tran
- Nan Jiang
Organizations
- Air Force Office of Scientific Research
- Florida State University
- National Science Foundation
- Oak Ridge National Laboratory