Modelling wave dispersion in fluid saturating periodic scaffolds
| Autor: | Robert Cimrman, Eduard Rohan |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
0209 industrial biotechnology
Discretization Floquet-Bloch wave decomposition 65Nxx homogenization FOS: Physical sciences 02 engineering and technology acoustic waves Homogenization (chemistry) Physics::Fluid Dynamics 020901 industrial engineering & automation porous media Inviscid flow Barotropic fluid 0202 electrical engineering electronic engineering information engineering FOS: Mathematics Mathematics - Numerical Analysis Dispersion (water waves) Physics wave dispersion Applied Mathematics Fluid Dynamics (physics.flu-dyn) 020206 networking & telecommunications Acoustic wave Mechanics Physics - Fluid Dynamics Numerical Analysis (math.NA) Finite element method Computational Mathematics Navier-Stokes equations Acoustic approximation |
| DOI: | 10.48550/arxiv.2101.01969 |
| Popis: | Acoustic waves in a slightly compressible fluid saturating porous periodic structure are studied using two complementary approaches: 1) the periodic homogenization (PH) method provides effective model equations for a general dynamic problem imposed in a bounded medium, 2) harmonic acoustic waves are studied in an infinite medium using the Floquet-Bloch (FB) wave decomposition. In contrast with usual simplifications, the advection phenomenon of the Navier–Stokes equations is accounted for. For this, an acoustic approximation is applied to linearize the advection term. The homogenization results are based the periodic unfolding method combined with the asymptotic expansion technique providing a straight upscaling procedure which leads to the macroscopic model defined in terms of the effective model parameters. These are computed using the characteristic responses of the porous microstructure. Using the FB theory, we derive dispersion equations for the scaffolds saturated by the inviscid, or the viscous, barotropic fluids, whereby the advection due to a permanent flow in the porous structures is respected. A computational study is performed for the numerical models obtained using the finite element discretization. For the FB methods-based dispersion analysis, quadratic eigenvalue problems must be solved. The numerical examples show influences of the microstructure size and of the advection generating an anisotropy of the acoustic waves dispersion. |
| Databáze: | OpenAIRE |
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