A high-order Discontinuous Galerkin Chimera method for laminar and turbulent flows

• Easy implementation: implementation as pre- and postproc. step to existing solvers.
• Consistent way of calculation of the BR2 fluxes and good approximation of gradients.
• Full linearization of Chimera operator gives similar costs as single grid calculation.
• Mass conservation is not strictly fulfilled but mass flow errors tend to zero.
• Robust calculation of turbulent flows with SA turbulence model.

In this study we present a Chimera scheme for the Discontinuous Galerkin method for the compressible Navier–Stokes equations as well as the Reynolds-Averaged Navier–Stokes (RANS) equations. For the turbulent simulations we use the Spalart–Allmaras one-equation turbulence model to close the RANS system. Focus of the study is the implementation of the Chimera scheme with a detailed description of all the necessary parts of the method: hole-cutting, definition of an interpolation operator and adaption of the time integration scheme. Concerning the time integration scheme the differences between explicit and implicit Chimera boundary conditions are elaborated for an implicit time-integration scheme solved with a Newton-GMRES method. The accuracy of the implemented method is tested with the method of manufactured solutions and an inviscid simulation of a Gaussian bump. The robustness and reliability is then assessed with a circular cylinder (Re=40Re=40) and a NACA0012 airfoil (Re=2.88·106Re=2.88·106) at different angles of attack. Both cases are run with a single grid and a Chimera grid version and compared with each other and with experimental and numerical reference data.