An ultra-weak method for acoustic fluid-solid interaction

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:213

Article

Huttunen, T.¹  Kaipio, J. P.¹  Monk, P.² 

[1] Univ Kuopio, Dept Phys, FI-70211 Kuopio, Finland

[2] Univ Delaware, Dept Math Sci, Newark, DE 19711 USA

关键词: fluid-solid interaction;    Helmholtz equation;    Navier equation;    finite element methods;    ultra-weak variational formulation;   

DOI  :  10.1016/j.cam.2006.12.030

来源: Elsevier

【 摘 要 】

We introduce the ultra-weak variational formulation (UWVF) for fluid-solid vibration problems. In particular, we consider the scattering of time-harmonic acoustic pressure waves from solid, elastic objects. The problem is modeled using a coupled system of the Helmholtz and Navier equations. The transmission conditions on the fluid-solid interface are represented in an impedance-type form after which we can employ the well known ultra-weak formulations for the Helmholtz and Navier equations. The UWVF approximation for both equations is computed using a superposition of propagating plane waves. A condition number based criterion is used to define the plane wave basis dimension for each element. As a model problem we investigate the scattering of sound from an infinite elastic cylinder immersed in a fluid. A comparison of the UWVF approximation with the analytical solution shows that the method provides a means for solving wave problems on relatively coarse meshes. However, particular care is needed when the method is used for problems at frequencies near the resonance frequencies of the fluid-solid system. (c) 2007 Elsevier B.V. All rights reserved.

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