Abstract: It is well accepted that the drag coefficients of incompressible flows past a sphere only depend on the Reynolds number Re. However, the influence of the Mach number Ma on the drag coefficient becomes increasingly obvious for flows with higher Mach numbers. Unfortunately, this influence has not yet been well understood. In this work, a numerical method coupling the hard-sphere and the pseudo-particle models (HS-PPM) is used to simulate flows past a sphere at 1≤Re≤20 and 0.1≤Ma≤3. The influences of the simulating domain and accommodation coefficients of the interactions between pseudo-particles and the solid sphere on drag coefficients are studied firstly. Then, approporiate simulation domains and reasonable accommodation coefficients are obtained to simulate flows past a sphere. Finally, based on the drag coefficients obtained from the HS-PPM simulations, a preliminary Mach-number correction model of drag coefficients is proposed.