[sharonyue]

It is know that (ANSYS Fluent theory guide page 375)

> The analytic scheme is very efficient. It can become inaccurate for large steps and in situations where the particles are not in hydrodynamic equilibrium with the continuous flow. The numerical schemes implicit and trapezoidal, in combination with Automated Tracking Scheme Selection, consider most of the changes in the forces acting on the particles and are chosen as default schemes. The runge-kutta scheme is recommended of nondrag force changes along a particle integration step.

I also found the analytical scheme is not accurate. However, I did not find any papers investigated on this subject. Any recommended papers?

Thanks