A new advection algorithm based on the scheme by MacCormack has been implemented in the atmospheric meso-y-scale model developed at the Department of Meteorology, Uppsala University. Prior to the implementation of the scheme, it was first tested in a simple advection model and in a shock wave model. The meso-y-scale model used to have a simple forward upstream scheme. The new scheme gives much less numerical dissipation compared to the upstream scheme, and this may cause reflection at the upper boundary. This is clearly seen in a simulation of airflow over bell-shaped terrain. This reflection was avoided when the model was provided with an upper boundary condition, proposed by Klemp and Durran, that permits radiation of internal gravity waves. In a simulation of a sea breeze circulation, the new scheme gives a sharper sea breeze front. It also gives a higher maximum wind speed and the maximum is reached earlier in the simulation. The grid in the meso-y-scale model 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. (C) 1994 Academic Press, Inc.