Formulation and Numerical Analysis of Acoustics Problems in Coupled Thermohydroelastic Systems

The coupled thermohydroelastic processes of acoustic wave and heat propagation in weak viscous fluid and elastic bodies form the basis of dissipative acoustics. The problems of dissipative acoustics have many applications in engineering practice, in particular in the development of appropriate medical equipment. This paper presents mathematical models for time and frequency domain problems in terms of unknown displacements and temperatures in both the fluid and the elastic body. Formulated corresponding variational problems and constructed numerical schemes for their solution based on the Galerkin approximations. The method of proving the well-posedness of the considered variational problems is proposed.