A time-dependent wave-thermoelastic solid interaction

George C. Hsiao, Tonatiuh Sánchez-Vizuet, Francisco Javier Sayas, Richard J. Weinacht

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

This paper presents a combined field and boundary integral equation method for solving the time-dependent scattering problem of a thermoelastic body immersed in a compressible, inviscid and homogeneous fluid. The approach here is a generalization of the coupling procedure employed by the authors for the treatment of the time-dependent fluid-structure interaction problem. Using an integral representation of the solution in the infinite exterior domain occupied by the fluid, the problem is reduced to one defined only over the finite region occupied by the solid, with nonlocal boundary conditions. The nonlocal boundary problem is analysed with Lubich's approach for time-dependent boundary integral equations. Existence and uniqueness results are established in terms of time-domain data with the aid of Laplace domain techniques. Galerkin semidiscretization approximations are derived and error estimates are obtained. A full discretization based on the convolution quadrature method is also outlined. Some numerical experiments in two dimensions are also included in order to demonstrate the accuracy and efficiency of the procedure.

Original languageEnglish (US)
Pages (from-to)924-956
Number of pages33
JournalIMA Journal of Numerical Analysis
Volume39
Issue number2
DOIs
StatePublished - Apr 23 2019
Externally publishedYes

Keywords

  • convolution quadrature
  • coupling BEM-FEM
  • fluid-structure interaction
  • Kirchhoff representation formula
  • retarded potential
  • time-domain boundary integral equation
  • variational formulation
  • wave scattering

ASJC Scopus subject areas

  • Mathematics(all)
  • Computational Mathematics
  • Applied Mathematics

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