Effects of Variable and Unequal Time Steps for Advective and Diffusive Processes in Simulations of the Urban Boundary Layer

Abstract

The two–dimensional, non-steady URBMET urban boundary layer model was integrated on a variable and staggered grid, with time–splitting and a donor cell advection scheme. Simulations for periods of up to 14 h of meteorological time were initially carried out using a constant time step for both the advection and diffusion processes, and using an eddy diffusivity which varies in space and time. The simulators were then repeated using a variable, but equal, time step for both By trial and error it was found that the minimum value of the time step normally associated with the diffusion term in the case of a constant eddy mixing coefficient in a constant, non-staggered grid could be exceeded by 50% without causing computational instability. The number of required time steps in the second series of runs, and thus the required computer time, was reduced by a factor of two from that needed for the first series. Results showed no significant changes from those resulting from the fixed time step simulations. Another series of simulations was carried out using unequal and variable time steps, with the advection process evaluated using a time step which was up to 20 times larger than that for the diffusion process. This change reduced the required computer time by an additional factor of three. Results showed an apparent reduction in the amount of numerically induced diffusion, and a corresponding enhancement in the strength of the circulation cells associated with the urban heat island. A final series of simulations demonstrated that anthropogenic moisture produces a significant buoyancy of the air above an urban area. This moisture enhanced the buoyancy produced by the urban heat island, and thus increased the intensity of the urban breeze effect.