In mesh-based numerical simulations, sweep is an important computation pattern. During sweeping a mesh, computations on cells are strictly ordered by data dependencies in given directions. Due to such a serial order, parallelizing sweep is challenging, especially for unstructured and deforming structured meshes. Meanwhile, recent high-fidelity multi-physics simulations of particle transport, including nuclear reactor and inertial confinement fusion, require {\em sweeps} on large scale meshes with billions of cells and hundreds of directions. In this paper, we present JSweep, a parallel data-driven computational framework integrated in the JAxMIN infrastructure. The essential of JSweep is a general patch-centric data-driven abstraction, coupled with a high performance runtime system leveraging hybrid parallelism of MPI+threads and achieving dynamic communication on contemporary multi-core clusters. Built on JSweep, we implement a representative data-driven algorithm, Sn transport, featuring optimizations of vertex clustering, multi-level priority strategy and patch-angle parallelism. Experimental evaluation with two real-world applications on structured and unstructured meshes respectively, demonstrates that JSweep can scale to tens of thousands of processor cores with reasonable parallel efficiency.