In this paper, a numerical method to accurately compute the vortical flows around high-alpha delta wings is proposed. The leading-edge vortex is captured by the adaptive grid refinement method coupled with the vortex-center identification. Effectiveness of this method is evaluated in the vortical flow with vortex breakdown. It is demonstrated that the adaptive grid refinement near the vortex center can significantly improve the accuracy of the vortex breakdown locations, as compared with the experiments. For the relatively small angle of attack case, the adaptive refinement at vortex core improves the surface pressure reasonably. This indicates the importance of the resolution at vortex core for accurate detection of the breakdown. The present numerical method, which combines the adaptive grid refinement method and the vortex core identification, is very effective for such a vortex dominated flow field.