Semin, Adrien ; Schmidt, Kersten (2016)
Absorbing boundary conditions for the viscous acoustic wave equation.
In: Math. Meth. Appl. Sci., 39 (17)
doi: 10.1002/mma.3755
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
We consider different acoustic models with viscosity in a semi-infinite waveguide with rigid walls, for which we propose and analyse absorbing boundary conditions on a truncated subdomain. The considered models are (i) the viscous acoustic equations in a stagnant mean flow, which exhibit for small viscosities boundary layers on the infinite walls, (ii) the limit equations for vanishing viscosity and (iii) a first-order approximation for low viscosity. The limit model (i) is well known as the Helmholtz equation for the pressure with homogeneous Neumann boundary conditions. For each of these models, the absorbing conditions appear as Dirichlet-to-Neumann (DtN) maps. The DtN boundary conditions for the singularly perturbed model (i) and the approximative model (iii) tend to the DtN boundary conditions of the limit problem (ii) if the viscosity approaches zero, and, hence, provide a uniform accuracy in the viscosity. The convergence of truncated DtN boundary conditions and the behaviour for viscosities tending to zero are shown in numerical experiments.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2016 |
| Autor(en): | Semin, Adrien ; Schmidt, Kersten |
| Art des Eintrags: | Bibliographie |
| Titel: | Absorbing boundary conditions for the viscous acoustic wave equation |
| Sprache: | Englisch |
| Publikationsjahr: | November 2016 |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Math. Meth. Appl. Sci. |
| Jahrgang/Volume einer Zeitschrift: | 39 |
| (Heft-)Nummer: | 17 |
| DOI: | 10.1002/mma.3755 |
| Kurzbeschreibung (Abstract): | We consider different acoustic models with viscosity in a semi-infinite waveguide with rigid walls, for which we propose and analyse absorbing boundary conditions on a truncated subdomain. The considered models are (i) the viscous acoustic equations in a stagnant mean flow, which exhibit for small viscosities boundary layers on the infinite walls, (ii) the limit equations for vanishing viscosity and (iii) a first-order approximation for low viscosity. The limit model (i) is well known as the Helmholtz equation for the pressure with homogeneous Neumann boundary conditions. For each of these models, the absorbing conditions appear as Dirichlet-to-Neumann (DtN) maps. The DtN boundary conditions for the singularly perturbed model (i) and the approximative model (iii) tend to the DtN boundary conditions of the limit problem (ii) if the viscosity approaches zero, and, hence, provide a uniform accuracy in the viscosity. The convergence of truncated DtN boundary conditions and the behaviour for viscosities tending to zero are shown in numerical experiments. |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Numerik und wissenschaftliches Rechnen |
| Hinterlegungsdatum: | 19 Nov 2018 21:05 |
| Letzte Änderung: | 19 Nov 2018 21:05 |
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