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

Tags

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Solar Physics