Mesh used in the paper "Robust Discontinuity Indicators for High-Order Reconstruction of Piecewise Smooth Functions."We have three types of spherical meshes: cubed-sphere (CS), quasi-uniform Voronoi (ICOD), and regionally refined (RRM) grids of the CS and ICOD types. They are NetCDF (.nc) meshes. Spherical meshes have different levels, from coarse to fine. All spherical meshes do not contain any function information.We also uploaded the general surfaces of the plane, cylinder, and reamer bit. They are VTK meshes. The grids in the general surfaces are the same, but they contain different function values and generated RDI information.