Space-time discontinuous Galerkin method for the solution of fluid-structure interaction

0498915 - ÚT 2019 RIV CZ eng J - Journal Article
Balázsová, M. - Feistauer, M. - Horáček, Jaromír - Hadrava, M. - Kosík, A.
Space-time discontinuous Galerkin method for the solution of fluid-structure interaction.
Applications of Mathematics. Roč. 63, Č. 6 (2018), s. 739-764. ISSN 0862-7940. E-ISSN 1572-9109
R&D Projects: GA ČR(CZ) GA16-01246S
Institutional support: RVO:61388998
Keywords : nonstationary compressible Navier-Stokes equations * time-dependent domain * arbitrary Lagrangian-Eulerian method * linear and nonlinear dynamic elasticity
OECD category: Acoustics
Impact factor: 0.537, year: 2018

The paper is concerned with the application of the space-time discontinuous Galerkin method (STDGM) to the numerical solution of the interaction of a compressible flow and an elastic structure. The flow is described by the system of compressible Navier-Stokes equations written in the conservative form. They are coupled with the dynamic elasticity system of equations describing the deformation of the elastic body, induced by the aerodynamical force on the interface between the gas and the elastic structure. The domain occupied by the fluid depends on time. It is taken into account in the Navier-Stokes equations rewritten with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. The resulting coupled system is discretized by the STDGM using piecewise polynomial approximations of the sought solution both in space and time. The developed method can be applied to the solution of the compressible flow for a wide range of Mach numbers and Reynolds numbers. For the simulation of elastic deformations two models are used: the linear elasticity model and the nonlinear neo-Hookean model. The main goal is to show the robustness and applicability of the method to the simulation of the air flow in a simplified model of human vocal tract and the flow induced vocal folds vibrations. It will also be shown that in this case the linear elasticity model is not adequate and it is necessary to apply the nonlinear model.
Permanent Link: http://hdl.handle.net/11104/0291522