A study evaluating unstructured mesh partitioning for computational fluid dynamics (CFD) simulations on parallel computers is presented. Considerations for effective partitioning of computational unstructured meshes for a family of implicit time-integration methods using the line-relaxation algorithm are outlined. Mesh partitioning using the Metis library is evaluated for two- and three-dimensional meshes. Different combinations of computational stencil information provided to the partitioning library are outlined and comparison of the resulted load balance and communication volume measures are presented. An augmentation to the existing mesh partitioning method via a heuristic algorithm is proposed. The heuristic algorithm relies on an initial partitioning of the mesh, which is then refined iteratively. Results using the new method are compared with the standard partitioning methods. This is done both from a theoretical perspective and by running the CFD code. Elapsed time results of the CFD code are presented from simulations on a parallel computer. Results show that the improved partitioning using the stencil information and the heuristic algorithm result in faster turn-around times. The stencil-based partitioning and the proposed heuristic algorithm are simple modifications to existing codes and are applicable to general simulations employing domain decomposition.