High order asymptotic expansion for the acoustics in viscous gases close to rigid walls
| dc.contributor.author | Schmidt, Kersten | |
| dc.contributor.author | Thöns-Zueva, Anastasia | |
| dc.date.accessioned | 2022-05-11T12:11:47Z | |
| dc.date.available | 2022-05-11T12:11:47Z | |
| dc.date.issued | 2012-07-11 | |
| dc.description.abstract | We derive a complete asymptotic expansion for the singularly perturbed problem of the acoustic wave propagation inside gases with small viscosity, this for the non-resonant case in smooth bounded domains in two dimensions. Close to rigid walls the tangential velocity shows a boundary layer of size $O(\sqrt{\eta})$ where $\eta$ is the dynamic viscosity. The asymptotic expansion based on the technique of multiscale expansion is in powers of $\sqrt{\eta}$ and takes into account curvature effects. The terms of the velocity and pressure expansion are defined independently by partial differential equations, where the normal component of velocities or the normal derivative of the pressure, respectively, are prescribed on the boundary. The asymptotic expansion is rigorously justified with optimal error estimates. | en |
| dc.identifier.issn | 2197-8085 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/16907 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-15685 | |
| dc.language.iso | en | |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
| dc.subject.ddc | 510 Mathematik | en |
| dc.subject.other | acoustic wave propagation | en |
| dc.subject.other | singularly perturbed PDE | en |
| dc.subject.other | asymptotic expansions | en |
| dc.title | High order asymptotic expansion for the acoustics in viscous gases close to rigid walls | en |
| dc.type | Research Paper | en |
| dc.type.version | submittedVersion | en |
| tub.accessrights.dnb | free | |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |
| tub.series.issuenumber | 2012, 04 | en |
| tub.series.name | Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin | en |
| tub.subject.msc2000 | 35C20 Asymptotic expansions | en |
| tub.subject.msc2000 | 35J25 Boundary value problems for second-order, elliptic equations | en |
| tub.subject.msc2000 | 41A60 Asymptotic approximations, asymptotic expansions | en |
| tub.subject.msc2000 | 35B40 Asymptotic behavior of solutions | en |
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