A novel high-order finite volume scheme using flux correction methods in conjunction with structured finite difference schemes is extended to low Mach and incompressible flows on strand grids. Flux correction achieves high-order by explicitly canceling low-order truncation error terms in the finite volume cell. The flux correction method is applied in unstructured layers of the strand grid. The layers are then coupled together using a source term containing the derivatives in the strand direction. Proper source term discretization is verified. Strand-direction derivatives are obtained by using summation-by-parts operators for the first and second derivatives. A preconditioner is used to extend the method to low Mach and incompressible flows. We further extend the method to turbulent flows with the Spalart Allmaras model. We verify high-order accuracy via the method of manufactured solutions, method of exact solutions, and physical problems. Results obtained compare well to analytical solutions, numerical studies, and experimental data. It is foreseen that future application in the Naval field will be possible.