Flow Feature Aligned Mesh Generation and Adaptation

Methods which allow for construction of flow feature aligned meshes in two- and three-dimensions have been developed in this thesis to investigate their potential for improvements in the numerical solution relative to globally refining the mesh. Of particular interest in the work is the generation of high-quality quadrilateral and hexahedral elements aligned with the dominant flow features. The two-dimensional techniques are applied on unstructured quad-dominant meshes, whilst the three-dimensional problems involve embedding high-quality hex-dominant mesh blocks into a hybrid volume mesh to improve their ability to capture anisotropic flow features such as shock waves, trailing shear layers/wakes and wing tip vortices. A method involving the medial axis has been studied to provide a geometric representation of two-dimensional flow features to allow feature-aligned meshes to be generated. Due to the flexibility of the approach, a range of complex features can be represented as simple geometric entities. These curves are embedded into the domain as virtual geometries to force alignment of unstructured quad-dominant surface mesh elements. The mesh locally mimics the attributes of a structured grid and provides high quality numerical solutions due to the alignment of the cell interfaces with the flow features. To improve the capability of hybrid meshes to resolve anisotropic flow physics, a method involving the extrusion of quad-dominant surface meshes has been developed. Surface meshes are extruded in the direction of extracted flow features, yielding feature-aligned semi-structured hex-dominant mesh blocks which can be embedded into the hybrid volume mesh. The presence of feature-aligned hexahedra has been shown to greatly enhance the resolution of anisotropic flow features compared with both isotropic and anisotropic tetrahedral elements, due to a significant reduction in numerical diffusion. Furthermore, improvements in the numerical solution have been also been obtained in a more efficient manner than isotropically refining the hybrid mesh. The results indicate that the type, orientation and size of the elements are significant contributing factors in the resolution of the dominant flow features.