Asymptotic analysis for acoustics in viscous gases close to rigid walls.

Kersten Schmidt, Anastasia Thöns-Zueva and Patrick Joly
Publication type:
Paper in peer-reviewed journals
Math. Models Meth. Appl. Sci., vol. 24(9), pp. 1823–1855
We derive a complete asymptotic expansion for the singularly perturbed problem of acoustic wave propagation inside gases with small viscosity. This derivation is for the non-resonant case in smooth bounded domains in two dimensions. Close to rigid walls the tangential velocity exhibits a boundary layer of size η where η is the dynamic viscosity. The asymptotic expansion, which is based on the technique of multiscale expansion is expressed in powers of the square root of η 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.
    author={Kersten Schmidt and Anastasia Thöns-Zueva and Patrick Joly },
    title={Asymptotic analysis for acoustics in viscous gases close to 
           rigid walls. },
    doi={10.1142/S0218202514500080 },
    journal={Math. Models Meth. Appl. Sci. },
    year={2014 },
    volume={24(9) },