A Lattice-adaptive Model for Solving Acoustic Wave Equations Based on Lattice Boltzmann Method
Publish Year: 1403
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_IJE-37-9_013
تاریخ نمایه سازی: 23 خرداد 1403
Abstract:
This paper addresses the need for an efficient and adaptable approach to solve linear acoustic wave equations in the lattice Boltzmann method (LBM). A novel lattice-adaptive model is introduced, derived through a Chapman–Enskog analysis, which utilizes a single relationship for the equilibrium distribution function across all lattice structures. The intended derivation begins by considering a standard equilibrium distribution function with unknown coefficients. By selecting the displacement of the acoustic wave as the zero-order microscopic moment, accurate recovery of the macroscopic wave equation is ensured. Unlike existing methods, the model simplifies the complexity associated with equilibrium distribution functions and offers greater versatility. The model is validated through extensive benchmark testing on one and two-dimensional wave propagation problems. Results demonstrate excellent agreement with analytical solutions, with maximum root mean square errors of ۱۰-۳ (<۰.۱% error) and minimum errors of ۱۰-۶ (<۰.۰۰۰۱% error), indicating high predictive accuracy (>۹۹.۹%). Additionally, the model exhibits second-order spatial accuracy, with the relative error norm E_۲ displaying slopes close to ۲, signifying a spatial accuracy of second order. The numerical simulations show a decrease in errors as the mesh size becomes more refined.
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Authors
A. Shahriari
Mechanical Engineering Department, University of Birjand, Birjand, Iran
S. A. Mirbozorgi
Mechanical Engineering Department, University of Birjand, Birjand, Iran
S. Mirbozorgi
Electrical and Computer Engineering Department, University of Alabama at Birmingham, Birmingham, USA
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