In this chapter we show the results from applying the hybrid grid technology to solve the Navier-Stokes equations. We modified an existing version of the code [30] to allow the use of quadrilaterals in two-dimensions and hexahedra, prisms, and pyramids in three-dimensions in addition to the original support for triangles and tetrahedra. The solvers needed minor modifications due to the general nature of the original code and the compatibility of the new element representation with the older C-based representation. We tested the new version of on simple physical models in order to verify the robustness of interfacing different element types together. We then extend the algorithm to be able to solve the Navier-Stokes equations in moving domains using the ALE formulation. We show that the numerical scheme is accurate for a moving domain test problem.