Flexible Infinite Element Formulation for Acoustic Simulation
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Solution Overview
Problem
Current methods for modeling transient (vibro-)acoustics wave propagation in unbounded domains are inefficient and complex, particularly for time-domain simulations, due to large time and memory requirements, complexity in implementation, and stability issues with existing formulations.
Innovation Solution
A novel flexible infinite element formulation that allows for the use of general convex-shaped envelopes, combined with the finite element method (FEM), to efficiently model time-domain propagation of sound waves in unbounded media. This formulation introduces a new auxiliary mapping between the radial coordinate and an auxiliary coordinate, enabling geometric flexibility and stability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional PML formulations are used for time-domain simulations, then acoustic wave absorption is achieved, but the number of degrees of freedom increases significantly and computational stability becomes difficult to guarantee
Solution Approach 1:
The patent transforms the PML formulation from frequency-domain to time-domain by changing the mathematical parameters and governing equations. This involves reformulating the absorbing boundary conditions to work with time-dependent wave equations, using auxiliary variables and differential operators that are compatible with time-stepping schemes. The transformation enables stable time-domain simulations while maintaining the essential wave-absorbing functionality.
Solution Approach 2:
The patent introduces auxiliary variables and intermediate mathematical constructs to bridge the gap between the original PML formulation and time-domain requirements. These intermediaries include additional differential operators and transformed coordinate systems that facilitate the transition to time-domain while controlling the increase in degrees of freedom through efficient numerical implementation.
2Measurement precision
If high-fidelity 3D simulation models are used, then simulation accuracy is improved, but computational cost and complexity increase
Solution Approach 1:
The patent divides the computational domain into distinct regions: the physical domain of interest and the PML absorption layer. This segmentation allows high-fidelity modeling only where necessary (in the physical domain) while using simplified absorbing boundary conditions in the PML region. The interface between these segments is carefully designed to maintain overall accuracy without requiring full high-fidelity modeling throughout the entire computational space.
Data Source
AI summary
A computer-implemented method for modeling acoustics of an object as a numerical simulation model in an unbounded domain to determine a field variable within a control volume of the unbounded domain includes providing a coordinate system mapping positions in the control volume. A geometrical specification of a sound source is provided in the control volume based on the coordinate system. To improve efficiency of numerically modelling transient acoustics wave propagation phenomena in unbounded domains, a convex shape is constructed around the sound source using Quickhull algorithm, infinite elements are extruded starting from the convex shape, and the coordinate system is transformed into a field variable coordinate system by mapping a radial coordinate of the coordinate system to an auxiliary coordinate extending from the convex shape to the infinite elements. Field shape functions are constructed using the auxiliary coordinate, and the field variable is determined by solving the numerical simulation model.