Time-Splitting Methods for Elastic Models Using Forward Time Schemes

Louis J. Wicker National Severe Storms Laboratory, Norman, Oklahoma

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William C. Skamarock National Center for Atmospheric Research,* Boulder, Colorado

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Abstract

Two time-splitting methods for integrating the elastic equations are presented. The methods are based on a third-order Runge–Kutta time scheme and the Crowley advection schemes. The schemes are combined with a forward–backward scheme for integrating high-frequency acoustic and gravity modes to create stable split-explicit schemes for integrating the compressible Navier–Stokes equations. The time-split methods facilitate the use of both centered and upwind-biased discretizations for the advection terms, allow for larger time steps, and produce more accurate solutions than existing approaches. The time-split Crowley scheme illustrates a methodology for combining any pure forward-in-time advection schemes with an explicit time-splitting method. Based on both linear and nonlinear tests, the third-order Runge–Kutta-based time-splitting scheme appears to offer the best combination of efficiency and simplicity for integrating compressible nonhydrostatic atmospheric models.

Corresponding author address: Dr. Louis J. Wicker, NOAA/NSSL, 1313 Halley Circle, Norman, OK 73069. Email: louis.wicker@nssl.noaa.gov

Abstract

Two time-splitting methods for integrating the elastic equations are presented. The methods are based on a third-order Runge–Kutta time scheme and the Crowley advection schemes. The schemes are combined with a forward–backward scheme for integrating high-frequency acoustic and gravity modes to create stable split-explicit schemes for integrating the compressible Navier–Stokes equations. The time-split methods facilitate the use of both centered and upwind-biased discretizations for the advection terms, allow for larger time steps, and produce more accurate solutions than existing approaches. The time-split Crowley scheme illustrates a methodology for combining any pure forward-in-time advection schemes with an explicit time-splitting method. Based on both linear and nonlinear tests, the third-order Runge–Kutta-based time-splitting scheme appears to offer the best combination of efficiency and simplicity for integrating compressible nonhydrostatic atmospheric models.

Corresponding author address: Dr. Louis J. Wicker, NOAA/NSSL, 1313 Halley Circle, Norman, OK 73069. Email: louis.wicker@nssl.noaa.gov

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