MATHEMATICA BOHEMICA, Vol. 137, No. 1, pp. 1-16, 2012

# On numerical solution of compressible flow in time-dependent domains

## Miloslav Feistauer, Jaromír Horáček, Václav Kučera, Jaroslava Prokopová

Miloslav Feistauer, Václav Kučera, Jaroslava Prokopová, Charles University Prague, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha 8, Czech Republic, e-mails: feist@karlin.mff.cuni.cz, vaclav.kucera@email.cz, jarkaprokop@post.cz; Jaromír Horáček, Institute of Thermomechanics, Academy of Sciences of the Czech Republic, Dolejškova 5, 182 00 Praha 8, Czech Republic, e-mail: jaromirh@it.cas.cz\emergencystretch2em

Abstract: The paper deals with numerical simulation of a compressible flow in time-dependent 2D domains with a special interest in medical applications to airflow in the human vocal tract. The mathematical model of this process is described by the compressible Navier-Stokes equations. For the treatment of the time-dependent domain, the arbitrary Lagrangian-Eulerian (ALE) method is used. The discontinuous Galerkin finite element method (DGFEM) is used for the space semidiscretization of the governing equations in the ALE formulation. The time discretization is carried out with the aid of a linearized semi-implicit method with good stability properties. We present some computational results for the flow in a channel, representing a model of glottis and a part of the vocal tract, with a prescribed motion of the channel walls at the position of vocal folds.

Keywords: compressible Navier-Stokes equations, arbitrary Lagrangian-Eulerian method, discontinuous Galerkin finite element method, interior and boundary penalty, semi-implicit time discretization, biomechanics of voice

Classification (MSC 2010): 65M60, 76M10, 76N15

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