Abstract: In the physics-based simulation of smoke,a set of Navier-Stokes partial differential equations need to be solved.In solving the problem,we use the Dimension Analysis method to simplify the equations. While solving the advection item,the semi-Lagrangian scheme is adopted.For the numerical dissipation inherent in the semi-Lagrangian scheme,a compact scheme highly accurate was introduced to improve the accuracy on coarse grids.It is shown that these methods can efficiently produce realistic results.