A Crank–Nicolson Leapfrog stabilization: unconditional stability and two applications

Nan Jiang ^[1] ; William Layton ^[1] ; Marina Moraiti ^[1] ; Michaela Kubacki ^[2] ; Hoang Tran ^[3]
1. [1] University of Pittsburgh
  
  University of Pittsburgh
  
  City of Pittsburgh, Estados Unidos
2. [2] Middlebury College
  
  Middlebury College
  
  Town of Middlebury, Estados Unidos
3. [3] Oak Ridge National Laboratory
  
  Oak Ridge National Laboratory
  
  Estados Unidos
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Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 281, Nº 1 (June 2015), 2015, págs. 263-276
Idioma: inglés
DOI: 10.1016/j.cam.2014.09.026
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Resumen
- We propose and analyze a linear stabilization of the Crank–Nicolson Leapfrog (CNLF) method that removes all time step/CFL conditions for stability and controls the unstable mode. It also increases the SPD part of the linear system to be solved at each time step while increasing solution accuracy. We give a proof of unconditional stability of the method as well as a proof of unconditional, asymptotic stability of both the stable and unstable modes. We illustrate two applications of the method: uncoupling groundwater–surface water flows and Stokes flow plus a Coriolis term.