An advection algorithm and an atmospheric airflow application (Q1339514)

The paper discusses computational experiments obtained from numerical tests of a new advection scheme in the MIUU meso-\(\gamma\)-model, developed at the Department of Meteorology of Uppsala University (MIUU). A critical evaluation of the results is presented, and a comparison of the results with those found from the application of other schemes (forward-upstream, Lax-Wendroff, Gadd, MacCormack, leapfrog) has been carried out. The improved MacCormack scheme suggested in this study involves a change both to the first and second step. The three most obvious ways are pointed out: in the first one, MC2a, gridpoints further outward are taken into consideration. Another way, MC2b, uses grid points on both sides of the original one. A third way, MC2c, is to take gridpoints towards the center into account. It turns out that the new scheme yields much less numerical dissipation compared to the upstream scheme. However, this may cause reflection at the upper boundary as noticed in a simulation of stably stratified airflow over mesoscale bell- shaped mountain ridges. This reflection was avoided when the model was provided with an upper boundary condition that permits radiation of internal gravity waves. Concerning a simulation of a sea breeze circulation, the new scheme gives a sharper sea breeze front. Moreover, it also gives a higher maximum wind speed, and the maximum is reached earlier in the simulation. The grid in the meso-\(\gamma\)-scale has also been staggered, the velocity components have all been moved a half grid interval from the location of the thermodynamic variables in the direction of the respective velocity component.