Some Accuracy Considerations for Simulating Large–Scale Atmospheric Flows with Time–Split Compressible Models

The use of time-split compressible models for simulating large-scale atmospheric flows is considered using the two-dimensional Eady instability problem as a test case. Preliminary results show that the classical time-splitting method of Klemp and Wilhelmson (1978) suffers from noticeable accuracy problems when using large grid spacings and large but stable time steps. The inaccuracies apparently relate to the use of implicit differencing in the vertical on the small time step and reflect an inability of the small-time-step cycle to properly adjust the pressure distribution when the time step is large. Analogous considerations are presented for several commonly used extensions of the Klemp and Wilhelmson method, including methods computing buoyancy on the small time step and methods using Runge-Kutta differencing on the large step. Some comparisons are also made to standard hydrostatic and incompressible formulations in an effort to evaluate relative accuracy and efficiency.