Simulating water for visual effects demands a high resolution surface with precise dynamics, but a fine discretization of the entire fluid volume is generally inefficient. Prior adaptive methods using octrees or unstructured meshes carry large overheads and im- plementation complexity. We instead show the potential of sticking with coarse regular Cartesian grids, using detailed cut cells at boundaries, and introducing a p-adaptive Discontinuous Galerkin method to discretize the pressure projection step in our fluid solver. This retains much of the data structure simplicity of regular grids, more efficiently captures smooth parts of the flow, and offers the flexibility to increase resolving power where needed.