Simulations of fluid flows over complex geometries are typically solved using a solution technique known as the overset meshing method. The geometry is meshed using grid types appropriate to the local geometry in a patchwork fashion, rather than meshing the entire geometry with one type of mesh. The strand-Cartesian approach is a simplification of this process. While high-order accurate solvers on Cartesian grids are simple to implement, strand grids are usually restricted to second-order accuracy, resulting in poor quality solutions. Flux correction is a high-order accurate solution method, specifically designed for use on strand grids. The flux correction method on strand grids is evaluated in conjunction with an overset Cartesian grid. Fundamental studies are considered which demonstrate the effectiveness of high-order methods in solving practical flows of interest.