Construction and examination of the total energy conservation

Because the advection term of atmospheric and oceanic equation systems is quasilinear, according a theory about construction of schemes, we summarize a new method of constructing the total energy conservation schemes by choosing different special functions. This study shows that not only many classical square conservation schemes can be derived too, but also difference schemes will be used flexibly for numerical simulation of atmospheric and oceanic systems. Furthermore, the concrete criterion for judging total energy conservation schemes is given. The numerical examination shows that these schemes keeps conservation features as much as possible under discretization.