Detailed Water with Coarse Grids: Combining Surface Meshes and Adaptive Discontinuous Galerkin

Figure 1: A simulation in a 25 × 25 × 25 grid generates thin splashes and sheets down to 1/1200 the domain width. We present a new adaptive fluid simulation method that captures a high resolution surface with precise dynamics, without an inef-ficient fine discretization of the entire fluid volume. Prior adap-tive methods using octrees or unstructured meshes carry large over-heads 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