The bubble packing method is implemented for adaptive mesh generation, particularly targeted for nonlinear multi-physics problems involving large gradients of field variables and a huge amount of computing time, such as welding and shear band problems. Numerical comparison is made with other automatic mesh generation to demonstrate the effectiveness of the bubble packing scheme for two- and three- dimensional domains. This illustrates the advantages of the present bubble packing scheme. It is shown that the bubble packing method provides meshes with high quality and affordable control of mesh density as well.