Abstract: It is in urgent necessity to introduce a high-efficient and robust numerical solution algorithm to deal with the slow convergence and poor robustness in the numerical calculation of axial flow cyclone. In this paper, a physical-mathematical model was established for axial flow cyclones. Then, three pressure-velocity coupling algorithms (i.e., SIMPLE, SIMPLEC and IDEAL) were adopted to perform numerical solution on cyclones. Finally, they were compared from the aspects of calculation efficiency and robustness. It is shown that the convergence and robustness of the IDEAL algorithm are superior to those of SIMPLE and SIMPLEC algorithms under different grid quantity, inlet velocity and turbulence model. Therefore, it is recommended to apply the high-efficient and robust IDEAL algorithm to the numerical calculation of cyclones. The research results provide the basis for the further study on the complex flowing characteristics of gas-liquid two-phase flow inside the cyclones and the prediction of separation performance.