Abstract: We present a new adaptive fluid simulation method that captures a high resolution surface with precise dynamics, without an inefficient fine discretization of the entire fluid volume. Prior adaptive methods using octrees or unstructured meshes carry large overheads and implementation complexity. We instead stick with coarse regular Cartesian grids, using detailed cut cells at boundaries, and discretize the dynamics with a p-adaptive Discontinuous Galerkin (DG) method. This retains much of the data structure simplicity of regular grids, more efficiently captures smooth parts of the flow, and offers the flexibility to easily increase resolving power where needed without geometric refinement.