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Expanded Stability through Higher Temporal Accuracy for Time-Centered Advection Schemes

Expanded Stability through Higher Temporal Accuracy for Time-Centered Advection Schemes Applying standard explicit time-differencing to hyperbolic equations (i.e., which characterize convection-dominated atmospheric flows) invariably results in rather severe stability restrictions. The primary problem appears to be attributable to the differencing approximation of the time derivative term. In this study the authors show that, for explicit, time-centered advection schemes, achieving higher-order temporal accuracy results in schemes with significantly improved stability properties compared with conventional leapfrog methods. Linear results show that marked improvement is possible in the stability properties by including in the differencing scheme a crucial term approximating the time derivative of third order. The critical CFL number for this time-centered Taylor (TCT) scheme is shown to exceed that of second-order leapfrog by nearly a factor of 2. Similar results hold for the corresponding fourth-order schemes. A solid-body rotation test confirms the findings of the two-dimensional stability analysis and compares these time-centered schemes with popular forward-in-time methods. One-dimensional nonlinear results corroborate the fundamental stablizing effect of the TCT approach with the TCT algorithm offering significant improvements in nonlinear stability over leapfrog methods as well as MacCormack’s scheme—a popular nonlinear, dissipative differencing scheme. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Monthly Weather Review American Meteorological Society

Expanded Stability through Higher Temporal Accuracy for Time-Centered Advection Schemes

Babarsky, Richard J.; Sharpley, Robert
Monthly Weather Review , Volume 125 (6) – Aug 14, 1995
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References (20)

Publisher
American Meteorological Society
Copyright
Copyright © 1995 American Meteorological Society
ISSN
1520-0493
DOI
10.1175/1520-0493(1997)125<1277:ESTHTA>2.0.CO;2
Publisher site
See Article on Publisher Site

Abstract

Applying standard explicit time-differencing to hyperbolic equations (i.e., which characterize convection-dominated atmospheric flows) invariably results in rather severe stability restrictions. The primary problem appears to be attributable to the differencing approximation of the time derivative term. In this study the authors show that, for explicit, time-centered advection schemes, achieving higher-order temporal accuracy results in schemes with significantly improved stability properties compared with conventional leapfrog methods. Linear results show that marked improvement is possible in the stability properties by including in the differencing scheme a crucial term approximating the time derivative of third order. The critical CFL number for this time-centered Taylor (TCT) scheme is shown to exceed that of second-order leapfrog by nearly a factor of 2. Similar results hold for the corresponding fourth-order schemes. A solid-body rotation test confirms the findings of the two-dimensional stability analysis and compares these time-centered schemes with popular forward-in-time methods. One-dimensional nonlinear results corroborate the fundamental stablizing effect of the TCT approach with the TCT algorithm offering significant improvements in nonlinear stability over leapfrog methods as well as MacCormack’s scheme—a popular nonlinear, dissipative differencing scheme.

Journal

Monthly Weather Review – American Meteorological Society

Published: Aug 14, 1995

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