Time-splitting methods for elastic models using forward time schemes

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.