We present the results of our numerical calculations that focus on the dynamics of anematic liquid crystal around a spherical particle imposing strong homeotropic anchoringat the surface. The first part of this article is devoted to the discussion of the effect of anexternal magnetic or electric field on the director configuration of a nematic liquid crystal.With the aid of an adaptive mesh refinement scheme, together with the tensor descriptionof the orientational order, for the first time in numerical calculations we successfullyreproduce the transition from a hyperbolic hedgehog defect to a Saturn ring defect,which was observed in a recent experiment. We also find that the trajectoriesof the defect core sensitively depend on the field strength. In the second partwe investigate how a hydrodynamic flow influences the orientational order of anematic liquid crystal around a particle carrying a hyperbolic hedgehog defect. Weobserve that for an intermediate Ericksen number, which characterizes the ratioof the viscous force to the elastic force of a nematic liquid crystal, the liquidcrystal is strongly convected by the flow, which results in a considerable elasticdistortion.