Mesh Generation Using Algebraic Volume Nodes
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Solution Overview
Problem
Current mesh generation methods for computational analysis of physical systems, particularly in complex configurations, are time-consuming and labor-intensive, especially when dealing with boundary layer flow simulations, and often result in meshing failures due to strict topology constraints in structured meshes and connectivity issues in unstructured meshes.
Innovation Solution
A method that generates a mesh of discrete nodes with algebraic volume nodes, where face area vectors are derived from discretized differential flux equations rather than geometrical equations, allowing for greater geometric flexibility and reducing the need for manual intervention, while maintaining the robustness and accuracy of structured or unstructured mesh solutions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If structured mesh methods are used, then numerical accuracy and stability are improved, but mesh generation flexibility and ease of handling complex geometry deteriorate
Solution Approach 1:
The patent segments the mesh into two distinct types: algebraic volume nodes (meshfree points without strict topology) and finite volume nodes (structured mesh with topology). This segmentation allows each type to be used in appropriate regions, combining the flexibility of meshfree methods with the accuracy of structured meshes.
Solution Approach 2:
The patent creates a unified mesh framework that can handle both algebraic volume nodes and finite volume nodes using the same numerical solution algorithms. This universality allows the system to accommodate complex geometries while maintaining numerical accuracy through the hybrid approach.
2Adaptability or versatility
If unstructured mesh methods are used, then mesh generation flexibility is improved, but reliability and stability of numerical solutions deteriorate
Solution Approach 1:
The patent segments the mesh into algebraic volume nodes (for flexibility) and finite volume nodes (for stability). By strategically placing different node types in different regions, the system achieves both mesh generation flexibility and numerical stability.
Solution Approach 2:
The patent changes the fundamental parameter of node connectivity from strict topology requirements (structured) to no topology requirements (meshfree), creating a spectrum of mesh types that can be optimized for different regions based on reliability requirements.
3Manufacturing precision
If manual intervention in mesh generation is increased, then mesh quality and suitability are improved, but productivity and time consumption deteriorate
Solution Approach 1:
The patent enables automated mesh generation by allowing the system to automatically select between algebraic volume nodes and finite volume nodes based on geometric characteristics. This self-service capability eliminates manual mesh generation while maintaining high mesh quality through algorithmic decision-making.
Solution Approach 2:
The patent automates the mesh generation process by dynamically adjusting mesh parameters and node types based on geometric input, replacing manual parameter adjustment with automated algorithms that achieve optimal mesh quality without human intervention.
4Measurement precision
If high aspect ratio anisotropic mesh is used for boundary layer, then accuracy of boundary layer flow simulation is improved, but device complexity and meshing difficulty deteriorate
Solution Approach 1:
The patent segments the computational domain into boundary layer regions (using algebraic volume nodes for flexibility) and outer regions (using finite volume nodes for structure). This segmentation enables high aspect ratio meshes in boundary layers without propagating complexity throughout the entire domain.
Solution Approach 2:
The patent applies different mesh qualities locally: high aspect ratio anisotropic meshing in boundary layer regions where it is most needed, while using more standard isotropic meshing in outer regions. This local quality approach maintains accuracy where required without unnecessarily increasing overall complexity.
Data Source
AI summary
In order to perform computational analysis of a physical system using a mesh of discrete nodes, for some of the nodes there are derived face area vectors between algebraic volumes associated with each algebraic volume node and neighbouring volumes in the mesh from solutions of discretized differential flux equations representing fluxes between the respective algebraic volume and each neighbouring volume. An integral form of the modelling equations representing relationships between physical properties of the physical system are discretized into volume equations in respect of volumes associated with respective nodes, using the derived face area vectors for the algebraic volumes, instead of finite volumes derived geometrically. Solution of the volume equations provides information on the physical properties of the physical system.