Abstract
A finite differencing scheme of invariant form for the shallow convection equations, which conserves momentum and total energy, is proposed. The proposed scheme is compared with another energy conserving scheme, i.e. that of flux form, with respect to their finite differencing expressions. It turns out that the scheme of invariant form is identical with that of flux form, if there are no computational errors in the continuity equation on every grid point. The scheme is tested and compared with that of flux form in the simulation of dry thermal, and it is confirmed that the scheme of invariant form conserves momentum and total energy as well as that of flux form.
