Flow Pattern Regular Expression via Graph Representation
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Solution Overview
Problem
Conventional methods for optimizing fluid structure design in flow fields face challenges due to high calculation times and costs, leading to limited search areas and potential for locally optimum solutions, where the word representation theory struggles to provide a unique correspondence to flow patterns.
Innovation Solution
A flow pattern regular expression creating method that uses a graph representation with a unique rooted, labeled, and directed tree to visualize structurally stable Hamiltonian vector fields, enabling one-to-one correspondence and allowing for the conversion of regular expressions into word representations, facilitating more efficient optimization designs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If word representation theory is used to represent flow patterns, then the complexity of representing flow patterns is reduced, but the precision of uniquely identifying specific flow patterns deteriorates
Solution Approach 1:
The flow pattern representation is segmented into two distinct components: word representations for topological classification and graph representations for precise structural identification. This segmentation allows each representation type to fulfill its strengths without compromise
Solution Approach 2:
Graph representations serve as an intermediary between the simplified word representations and the detailed flow pattern structures. The graph representation captures the precise topological relationships that word representations cannot uniquely specify
2Measurement precision
If conventional fluid simulation methods are used for structure optimization, then the accuracy of flow field analysis is improved, but the calculation time and design costs increase
Solution Approach 1:
Instead of repeatedly performing full fluid simulations, the invention creates graph representations that copy and preserve the essential topological features of flow patterns. These graph copies can be analyzed and compared without requiring computationally expensive simulations
Solution Approach 2:
The invention changes the representation parameter from continuous flow field data requiring large-scale numerical calculation to discrete graph structures capturing topological relationships, thereby reducing computational complexity while maintaining analytical accuracy
3Productivity
If the search area for optimization is limited to reduce calculation time, then the productivity of the design process is improved, but the reliability of obtaining the global optimum deteriorates
Solution Approach 1:
The graph representation method serves multiple functions simultaneously: it enables rapid classification of flow patterns, facilitates comparison across different design configurations, and provides a framework for exploring broader search spaces without proportional increases in computational cost
Data Source
AI summary
There is provided a flow pattern regular expression creating method, a regular expression creating apparatus, and a program enabling provision of a new representation method enabling one-to-one correspondence to a flow pattern. A regular expression creating method of creating a regular expression of a flow pattern in a multiply connected exterior domain with N (N is an integer equal to or larger than 1) holes topologically includes a graph representation creating step of creating a graph representation having one-to-one correspondence to the flow pattern; and a regular expression creating step of creating a regular expression from the graph representation that is created at the graph representation creating step.