Geometric Representation of Flow Features Using the Medial Axis for Mesh Generation

Abstract

A method to represent complex flow features as geometric entities, using the medial axis for the purpose of generating flow-feature aligned meshes, is presented. These geometric entities are embedded into the domain to influence the generation of unstructured quad-dominant surface meshes in two and three dimensions. The resulting high-quality feature-aligned surface meshes can locally mimic the attributes of a structured grid. This paper also presents a method to extrude shock-aligned quad-dominant surface meshes beyond the boundary layer to cover the extent of transonic shock waves. The process provides a means to embed a high-quality hex-dominant mesh block, aligned with the transonic shock wave, into a hybrid volume mesh for viscous computations. Inclusion of the aligned mesh block is shown to enhance the ability of the hybrid mesh to resolve the shock wave, and thus, improve the numerical solution.Nomenclature a = speed of sound M n = normal Mach number R 2 = polynomial-fit-quality measure r 1 , r 2 = background-source radii of influence S = point set s, s 0 = background-source mesh-spacing values V = velocity vector α = radius size in α-shape computation β = angle between neighboring medial-axis branches ∇p = pressure gradient

Modified multi-dimensional limiting process with enhanced shock stability on unstructured grids

“…Unstructured grids are commonly used for spatial discretizations by current industrial computational fluid dynamics codes that simulate aerodynamics or gas dynamics phenomena. The advantages of unstructured grids include the conveniences in automatic grid generation [1,2,3], grid adaptation [4,5,6], moving mesh techniques [7,8], for complex geometries and flow phenomena. The application of unstructured grids significantly facilitates the aforementioned aspects.…”

Cross-Field Structured Adaptive Mesh Using Medial Axis Flow Feature Extraction

“…Step 4 in Section 3.2, proposed by Harris et al [6,7], which mainly consists of three steps: marking flow feature nodes, recognizing boundaries based on α-shape, and extracting flow feature curves based on medial axis. Grid adaptive criteria and flow feature nodes marking are carried out using the Hessian matrix, while flow feature curve extraction is handled using the medial axis approach.…”

“…Taking blocks in Fig. 11 as an example, the associated boundaries should be (1,3,6), (8,9,11), (2,4,10), (5,7,12).…”

“…Nevertheless, the method poses a challenge that the extraction of features is hard to achieve when the flow structures become complex. Therefore, to increase flexibility and capability of handling more intricate cases, Harris and Qin [6,7] followed along the line of feature aligned mesh adaption and made use of medial axis to represent complex flow structures as geometric entities after the flow field solution. The medial curves are embedded in the domain to guide the generation of an unstructured high-quality anisotropic quadrilateral mesh, which is locally aligned with flow features.…”

Sequential feature‐based mesh movement and adjoint error‐based mesh refinement

“…More recently, mesh regeneration based on the Hessian of flow quantities has started to gain more and more popularity. One of the two approaches proposed is that of References 9,21,22. In this case, features are identified by combining flow parameters and then fully quadrilateral/hexahedral high-quality blocks are placed around them.…”