Numerical Simulation of Compressible Vortical Flows Using a Conservative Unstructured-Grid Adaptive Scheme (Communications in Computational Physics, 2012)
A two-dimensional numerical scheme for the compressible Euler equationsis presented and applied here to the simulation of exemplary compressible vorticalflows. The proposed approach allows to perform computations on unstructured moving grids with adaptation, which is required to capture complex features of the flow-field. Grid adaptation is driven by suitable error indicators based on the Mach numberand by element-quality constraints as well. At the new time level, the computationalgrid is obtained by a suitable combination of grid smoothing, edge-swapping, gridrefinement and de-refinement. The grid modifications—including topology modification due to edge-swapping or the insertion/deletion of a new grid node—are interpreted at the flow solver level as continuous (in time) deformations of suitably-definednode-centered finite volumes. The solution over the new grid is obtained without explicitly resorting to interpolation techniques, since the definition of suitable interfacevelocities allows one to determine the new solution by simple integration of the Arbitrary Lagrangian-Eulerian formulation of the flow equations. Numerical simulationsof the steady oblique-shock problem, of the steady transonic flow and of the start-upunsteady flow around the NACA 0012 airfoil are presented to assess the scheme capabilities to describe these flows accurately.