Adaptive Solution of Viscous Aerodynamic Flows Using Unstructured Grids

grantor: University of TorontoUnstructured grids are used in numerical models applied to aerodynamic design for their ability to conform easily to complex geometries. Their lack of rigid connectivity allows the grid generation process to be highly automated, reducing the expertise needed. The unstructured grid is ideally suited for local refinement based on the flow field solution, providing an opportunity for faster, less memory intensive operation for a specific level of accuracy. The purpose of this research is to develop such an algorithm using solution-adaptive unstructured triangular grids to solve the compressible Navier-Stokes equations on two-dimensional airfoil profiles. The basic solver utilizes a finite-volume methodology with Runge-Kutta time marching to produce steady-state solutions. An improved artificial dissipation method is developed that provides reduced grid sensitivity and improved accuracy for high-aspect-ratio grids. The solution-adaptive gridding method identifies under-resolved regions of the solution through an adaptation parameter based on normalized grid edge differences of the flow field variables. New grid nodes are added in regions where the magnitude of the adaptation parameter is greatest, yielding a local grid refinement. The high-aspect-ratio nature of the grid in viscous regions of the flow is preserved after adaptation through the development of a solution-dependent retriangulation routine. Several test cases on laminar and turbulent flows are presented that demonstrate the performance of the algorithm. It is shown that the adaptation configuration that achieves the greatest improvement in resolution uses an adaptation parameter consisting of a combination of Mach number and density edge differences, with 55% of the adapted nodes added in the first pass and 45% in the second to yield a four-fold increase in the number of grid nodes. The test cases also demonstrate that the adaptation routine is capable of providing at least a 40% reduction in lift and pressure drag coefficient errors over all flow regimes compared to solutions obtained on unadapted grids with an equivalent number of nodes. The effectiveness of the algorithm as a design tool is realized in a final comparison of an adapted solution to experimentally determined results on a complex three-element airfoil configuration.Ph.D