Journal
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 24, Issue 9, Pages 1823-1855Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202514500080
Keywords
Acoustic wave propagation; singularly perturbed PDE; asymptotic expansions
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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 O(root eta) where. is the dynamic viscosity. The asymptotic expansion, which is based on the technique of multiscale expansion is expressed in powers of v. 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.
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