Abstract
Crowley's second- and fourth-order nonconservative techniques for treating the advection term in numerical solutions of the hydrothermodynamic equations are tested on a model of cumulus cloud growth over mountains. The results are compared with previous integrations using upstream differencing, a first-order method.
All three methods give comparable results on a symmetric case. However, numerical damping which is a characteristic of the upstream-differencing method is considerably reduced in the Crowley techniques, as evidenced by curves of kinetic energy changes and sources and sinks for this energy.
In an ambient wind case the Crowley second-order method and the upstream-differencing method give comparable results if the eddy diffusion coefficients used in the Crowley method are twice as large as those used in the upstream-differencing method.
The results illustrate that the value of the eddy coefficients is crucial for the formation of the numerical clouds in the ambient wind model. Coefficients that are too small or too large lead to weak circulation cells created by the heated slopes and insufficient penetration into the upper flow region to form a cloud.
The smaller numerical diffusion of the Crowley second-order method is illustrated in a test of the numerical diffusion of rainwater in the cloud model. Upstream differencing causes rainwater contents downwind an order of magnitude larger than those that occur using the Crowley technique for advection.
