Tracing the paths of collections of particles through a flow field is a key step for many flow visualization and analysis methods. When a flow field is interpolated from the nodes of an unstructured mesh, the process of advecting a particle must first find which cell in the unstructured mesh contains the particle. Since the paths of nearby particles often diverge, the parallelization of particle advection quickly leads to incoherent memory accesses of the unstructured mesh. We have developed a new block advection GPU approach that reorganizes particles into spatially coherent bundles as they follow their advection paths, which greatly improves memory coherence and thus shared-memory GPU performance. This approach works best for flows that meet the CFL criterion on unstructured meshes of uniformly sized elements, small enough to fit at least two timesteps in GPU memory.