Towards automatic grid independent viscous solutions with an adaptive Cartesian/Quad grid flow solver

Abstract

A hybrid adaptive Cartesian/adaptive Quad (quadrilateral) (ACAQ) grid method has been developed to simulate viscous flows. The adaptive Quad grids are generated around solid bodies, so that non-isotropic grid adaptations can be used to resolve the viscous boundary layers. Quadtree data structures are used to represent both the Cartesian and Quad grids. The generation of the Cartesian grid begins with a single cell; the Quad grid starts with very coarse cells corresponding to a forest of Quadtrees. Both the Cartesian and Quad grids are then produced through recursive Quadtree sub-divisions. Cell-cutting is used to “merge” the Cartesian/Quad grids into a single computational grid. A cell-centered finite volume flow solver, with a least squares reconstruction scheme and Roe’s flux splitting has been developed. A scheme for the viscous fluxes is presented. Grid adaptations are carried out to place control volumes where required the most, achieving maximum accuracy with minimum cost. An accuracy study and several test cases are included to demonstrate the capability of the methodology.