A triangular cut-cell adaptive method for high-order discretizations of the compressible Navier–Stokes equations

This paper presents a mesh adaptation method for higher-order ( p > 1 ) discontinuous Galerkin (DG) discretizations of the two-dimensional, compressible Navier–Stokes equations. A key feature of this method is a cut-cell meshing technique, in which the triangles are not required to conform to the boundary. This approach permits anisotropic adaptation without the difficulty of constructing meshes that conform to potentially complex geometries. A quadrature technique is proposed for accurately integrating on general cut cells. In addition, an output-based error estimator and adaptive method are presented, appropriately accounting for high-order solution spaces in optimizing local mesh anisotropy. Accuracy on cut-cell meshes is demonstrated by comparing solutions to those on standard, boundary-conforming meshes. Robustness of the cut-cell and adaptation technique is successfully tested for highly anisotropic boundary-layer meshes representative of practical high Re simulations. Furthermore, adaptation results show that, for all test cases considered, p = 2 and p = 3 discretizations meet desired error tolerances using fewer degrees of freedom than p = 1 .