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

Applications of mathematics

Monika Balázsová^1¹  Miloslav Feistauer^1² 

[1] Charles University, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha 8, Czech Republic^1;Institute of Thermomechanics, Academy of Sciences of the Czech Republic, Dolejškova 5, 182 00 Praha 8, Czech Republic^2

关键词: nonstationary compressible Navier-Stokes equations;    time-dependent domain;    arbitrary Lagrangian-Eulerian method;    linear and nonlinear dynamic elasticity;    space-time discontinuous Galerkin method;    vocal folds vibrations;   

DOI  :  10.21136/AM.2018.0139-18

学科分类：应用数学

来源: Akademie Ved Ceske Republiky

【 摘 要 】

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.

【 授权许可】

Unknown