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Some aspects of the symmetrization of the contained compressible-fluid vibration eigenproblem. (English) Zbl 0595.76069
Innovative numerical methods in engineering, Proc. 4th Int. Symp., Atlanta/Ga. 1986, 249-254 (1986).
Summary: [For the entire collection see Zbl 0587.00014.]
The problem of coupled vibrations of an acoustic fluid enclosed in an elastic container is considered. The container structure is discretized by a displacement finite element formulation and the acoustic fluid by a displacement-potential finite element formulation.
The vibrations of this coupled system are governed by an unsymmetric algebraic eigenvalue problem. Matrix-scaling procedures derived in another paper lead to several symmetric forms of the eigenproblem.
This note show that these forms are computationally equivalent if the problem includes a specified-pressure boundary condition, such as a free surface. If all fluid boundary conditions are natural, some symmetric forms lead to numerical difficulties associated with the presence of a constant-potential spurious mode.

MSC:
76Nxx Compressible fluids and gas dynamics, general
76Q05 Hydro- and aero-acoustics