A TIME-SPLITTING SCHEME FOR THE ELASTIC EQUATIONS INCORPORATING 2ND-ORDER RUNGE-KUTTA TIME DIFFERENCING

A forward-in-time splitting method for integrating the elastic equatio ns is presented. A second-order Runge-Kutta time integrator (RK2) for the large-time step integration is combined with the forward-backward scheme in a manner similar to the Klemp and Wilhelmson method. The new scheme produces fully second-order-accurate integrations for advectio n and gravity wave propagation. The RK2 scheme uses upwind discretizat ions for the advection terms and is easily combined with standard vert ically semi-implicit techniques so as to improve computational efficie ncy when the grid aspect ratio becomes large. A stability analysis of the RK2 split-explicit scheme shows that it is stable for a wide range of advective and acoustic wave Courant numbers. The RK2 time-split sc heme is used in a full-physics nonhydrostatic compressible cloud model . The implicit damping properties associated with the RK2's third-orde r horizontal differencing allows for a significant reduction in the va lue of horizontal filtering applied to the momentum and pressure field s, while qualitatively the solutions appear to be better resolved than solutions from a leapfrog model.