We present the results of our numerical attempts to simulate the configuration of a nematic liquid crystal around a spherical particle. We focus on the effect of an external field, such as a magnetic field or a flow field, on the director configuration and the topological defects accompanied by the particles. The use of adaptive mesh refinement together with a tensor order parameter for the description of the orientational order makes it feasible to tract the dynamics of a nematic liquid crystal without any special treatment of the topological defects. © 2004 American Institute of Physics