This work is conducted towards the accurate prediction of compressor tip vortex. Accurate computation of highly vortical flow is affected by many parameters, such as numerical scheme and turbulence model. In this work the effect of numerical scheme is studied using mesh refinement study and comparison of numerical results from central scheme and a newly developed high order upwind scheme. Behaviors of numerical methods in the tip vortex region are also theoretically and numerically analyzed. It is found the computed tip vortex is significantly affected by mesh resolution and numerical dissipation. Currently widely numerical strategy, i.e., mesh with moderate resolution and low order scheme would yield quite inaccurate result. Predicted tip vortex is always dissipated earlier and this highlights the advantage of high order scheme in predicting detailed flow features. Besides coarser mesh and low order method, analysis of numerical methods reveals a new finding, in that the designed order of accuracy is not guaranteed in the tip vortex region. For central scheme pressure based shock sensor is unnecessarily activated and excessive artificial dissipation is added. For high order upwind scheme it tends to use low order reconstruction and new method considering flow physics shows its improved vortex prediction capability. Conclusions from this work can be used in future numerical studies about tip vortex to improve the numerical accuracy.