When the convection-dominated Burgers equation is solved by use of the difference method, the computational accuracy of many usual difference schemes will lower.The designre-quirements of difference scheme of the non-linear convection term are presented, and some new difference schemes, which is known as follow-flow schemes, are obtained in this paper, in order to raise the computational accuracy of convection-dominated equation. The advantages of the follow-flow schemes are shown by means of some examples in this paper.

At first, the three-dimensional vector potential and vorticity function are introduced, and the vector potential and vorticity equations are obtained in the case of arbitrary variation between density and temperature of water. Then, the vector potential and vorticity equations and the method of the false transient are applied to compute the three-dimensional viscous natural convection. Finaly, the effect of the property of unusual variation between density and temperature of water on three-dimensional natural convection is analysed and discussed by use of typical examples.