Convected Perfectly Matched Layers for Irregular Radiating Bodies
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Solution Overview
Problem
Current perfectly matched layer (PML) techniques for non-reflective boundary conditions in numerical simulations are limited by restrictive geometry requirements, limited coordinate-stretching options, and complexity in implementation, making them inefficient and user-unfriendly, especially when modeling irregular radiating bodies.
Innovation Solution
The development of a convected perfectly matched layer (PML) expression that allows for automatic definition of boundary conditions in arbitrary directions, independent of mean flow geometry, enabling efficient absorption of acoustic waves and accommodating both constant and non-constant mean flows, thereby simplifying the implementation process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If traditional PML is used with constant stretching aligned with coordinate axes, then implementation is simpler, but the boundary condition shapes are limited to boxes, cylinders, or spheres which cannot efficiently surround irregular radiating bodies
Solution Approach 1:
The patent introduces dynamic coordinate stretching where the stretching direction and magnitude can vary spatially and arbitrarily, rather than being fixed along coordinate axes. This allows the PML to adapt to irregular geometries by defining stretching vectors that follow the radiation pattern of the source, enabling efficient surrounding of complex radiating bodies while maintaining mathematical tractability through the dynamic stretching formulation
Solution Approach 2:
The patent extends the traditional PML approach by introducing arbitrary directional stretching beyond the fixed coordinate system. This adds a dimensional freedom where stretching can occur in any direction defined by unit vectors, allowing the PML to conform to irregular shapes while the automatic definition procedure handles the increased complexity through systematic calculation of stretching parameters
2Productivity
If PML is used to efficiently absorb acoustic waves, then computational degrees of freedom should be minimized, but regular shapes must be large to surround irregular radiating bodies which increases the total number of degrees of freedom
Solution Approach 1:
By implementing dynamic stretching that follows the radiation characteristics of irregular bodies, the PML can be positioned closer to the source without causing reflections. This reduces the distance between the radiating body and the PML boundary, thereby reducing the overall domain volume and computational degrees of freedom while maintaining absorption efficiency
Solution Approach 2:
The patent applies local stretching properties where the stretching direction and magnitude are tailored to the local geometry and radiation pattern at each boundary location. This allows the PML to efficiently absorb waves in the specific directions where radiation occurs, reducing the required PML thickness and overall domain size compared to uniform stretching approaches
3Ease of operation
If traditional PML with limited coordinate-stretching is used, then fewer parameters need to be defined, but user-friendliness deteriorates and implementation becomes complicated for irregular geometries
Solution Approach 1:
The patent implements an automatic definition procedure that calculates the appropriate stretching parameters based on the geometry of the radiating body and the desired PML characteristics. The system automatically determines the stretching directions, magnitudes, and PML thickness without requiring manual specification of multiple parameters, making the method user-friendly while handling irregular geometries efficiently
Solution Approach 2:
The patent creates a universal PML formulation that works for both regular and irregular geometries, constant and varying mean flows, and different radiation patterns. The automatic definition procedure and arbitrary stretching capability make the method broadly applicable across different scenarios without requiring separate parameter sets or manual adjustments for each case
Data Source
AI summary
Systems, apparatuses, and methods are described relating to object modeling, including, but not limited to, providing a convected perfectly matched layer (PML) expression as boundary condition for at least a portion of a model. The convected PML expression defines the boundary condition of the portion of the model in any arbitrary direction, allowing automatic definition of the boundary condition. The convected PML expression defines the boundary condition of the portion of the model in a constant or non-constant mean flow context.