Nonlinear solution adaptive structured grids via heat-conduction analogies

This paper discusses an adaptive grid approach, developed using Fortran 77, on quadrilateral meshes for the Euler and Navier-Stokes solvers. Solution adaptation is through two nonlinear heat-conduction analogies applied directly on a two-dimensional surface using the finite volume method. Clustering of the grid generated is controlled by the conductivity in the computational domain, which is related arbitrarily to the geometrical curvature and flow gradient. Three levels of “multigrid” approach are implemented to accelerate convergence as a grid refinement process. The grid quality is accessed by a histogram analysis of maximum angle and aspect ratio distributions within the computational domain. This work assumes that interpolation errors due to numerical approximation of fluxes across the surfaces of a control volume should become significant as the skew angle and aspect ratio increases. Detailed computational results and comparisons with measured data are presented for steady transonic flow over a NACA0012 airfoil, supersonic flow through a DFVLR rotor, and a 15° ramp.