Calculations were carried out on two test cases: the convection of a wave at constant speed in a square domain, and the convection of material lines about a cylinder using a potential-flow velocity field. The square domain was tested on two different mesh sizes. The first mesh has 1,514 cells and the second mesh has 13,776 cells. Only one mesh was available for the cylinder, and it has 57,575 cells. The effects of the mesh size will be discussed and analyzed using the square problem, and these results are compared against the exact analytical solution. A comparison between the structured- and unstructured-grid solutions will be made using the cylinder domain since no exact solution exist for this case.