Anisotropic Polyhedral Boundary Layer Adaptation
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Solution Overview
Problem
Conventional mesh refinement algorithms are limited in their ability to adaptively refine polyhedral meshes, leading to inefficient computational efforts and lack of precision, especially in boundary layers where anisotropic refinement is needed, while existing methods often waste resources by refining equally in all directions.
Innovation Solution
An anisotropic polyhedral boundary layer adaptation method that refines polyhedral prisms along specific directions, allowing for seamless transitions between anisotropic and isotropic regions, and combining normal and tangent refinement methods to achieve efficient mesh density and accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If isotropic refinement is used to split elements equally in all directions, then the solution accuracy is improved, but computational effort is wasted by refining elements where refinement is not required
Solution Approach 1:
The patent applies local quality by implementing anisotropic refinement that adapts mesh element size and shape to local solution characteristics. The algorithm identifies regions requiring refinement based on solution gradients and curvature, then applies targeted refinement only where needed, rather than uniformly refining all elements. This resolves the contradiction by improving solution accuracy in critical regions while avoiding unnecessary computational effort in regions where the solution is already sufficiently resolved.
Solution Approach 2:
The patent employs dynamic adaptation through iterative refinement cycles where the mesh is continuously adjusted based on solution feedback. The refinement criteria are evaluated at each iteration, and the mesh topology is dynamically modified to optimize resolution where required. This dynamic approach allows the method to concentrate computational resources on regions requiring higher accuracy while maintaining efficiency overall.
2Manufacturing precision
If isotropic refinement is applied to boundary layer elements, then mesh density increases uniformly, but the directional resolution needed for boundary layer accuracy is lost
Solution Approach 1:
The patent applies asymmetry by implementing anisotropic refinement that creates non-uniform mesh elements with different dimensions in different directions. For boundary layers, the algorithm generates elongated elements stretched in the direction parallel to the surface while maintaining fine resolution in the normal direction. This asymmetric element configuration captures the directional nature of boundary layer physics, resolving the contradiction between achieving proper boundary layer resolution and maintaining computational efficiency.
Solution Approach 2:
The patent utilizes parameter changes by dynamically adjusting mesh element parameters (size, shape, orientation) based on local flow conditions and boundary layer characteristics. The refinement algorithm modifies element aspect ratios and dimensions to match the physical requirements of boundary layer resolution, transitioning from isotropic to anisotropic parameters where needed. This allows the mesh to adapt its parameters to achieve both boundary layer accuracy and computational efficiency.
3Measurement precision
If mesh density is increased throughout the entire mesh, then solution accuracy improves, but computational cost increases significantly
Solution Approach 1:
The patent applies partial action by implementing selective refinement that increases mesh density only in specific regions where solution accuracy requires it, rather than uniformly increasing density throughout the entire mesh. The algorithm identifies critical regions based on solution gradients, curvature, and physical phenomena, then applies refinement only to those regions. This resolves the contradiction by achieving necessary solution accuracy in critical areas while avoiding the computational overhead of refining the entire mesh.
Solution Approach 2:
The patent employs segmentation by dividing the computational domain into regions with different refinement requirements. The mesh is segmented into fine-resolution regions where accuracy is critical and coarse-resolution regions where lower detail is acceptable. This segmented approach allows the method to concentrate computational resources on regions requiring high accuracy while maintaining a coarser, more efficient mesh in other areas, thus resolving the contradiction between solution accuracy and the number of mesh elements.
Data Source
AI summary
Machine assisted systems and methods for anisotropic polyhedral boundary layer adaptation that provides an anisotropic refinement of polyhedral prisms are described. The method can include operations: identifying a prismatic polyhedral cell as a parent cell within a polyhedral mesh representing an object of a physical system; generating a plurality of child cells for the parent cell based on non-overlapping child faces of a side face as a parent face, wherein a pair of mid-edge nodes for the side face are connected anisotropically for a child face edge of the non-overlapping child faces, the pair of mid-edge nodes are connected between the two base edges or between the two side edges; and refining the polyhedral mesh until a refinement level or a size limit is obtained, wherein the refining the polyhedral mesh includes the identification of the prismatic polyhedral cell and the generation of the plurality of child cells.