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This study deals with the development of an accurate, efficient and robust method for the numerical solution of the interaction of compressible flow and nonlinear dynamic elasticity. This problem requires the reliable solution of flow in time-dependent domains and the solution of deformations of elastic bodies formed by several materials with complicated geometry depending on time. In this paper, the fluid–structure interaction (FSI) problem is solved numerically by the space-time discontinuous Galerkin method (STDGM). In the case of compressible flow, we use the compressible Navier–Stokes equations formulated by the arbitrary Lagrangian–Eulerian (ALE) method. The elasticity problem uses the non-stationary formulation of the dynamic system using the St. Venant–Kirchhoff and neo-Hookean models. The STDGM for the nonlinear elasticity is tested on the Hron–Turek benchmark. The main novelty of the study is the numerical simulation of the nonlinear vocal fold vibrations excited by the compressible airflow coming from the trachea to the simplified model of the vocal tract. The computations show that the nonlinear elasticity model of the vocal folds is needed in order to obtain substantially higher accuracy of the computed vocal folds deformation than for the linear elasticity model. Moreover, the numerical simulations showed that the differences between the two considered nonlinear material models are very small. [ABSTRACT FROM AUTHOR]

The subject of the paper is the numerical simulation of two-phase flow of immiscible fluids. Their motion is described by the incompressible Navier-Stokes equations with different constant density and viscosity for different fluids. The interface between the fluids is defined with the aid of the level-set method using a transport first-order hyperbolic equation. The Navier-Stokes system is equipped with initial and boundary conditions and transmission conditions on the interface between the two fluids. This system is discretized by the Taylor-Hood P2/P1 conforming finite elements in space and the second-order BDF method in time. The transport level-set problem is solved with the aid of the space-time discontinuous Galerkin method. Numerical experiments demonstrate that the developed method is accurate and robust. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical simulation of the interaction of compressible viscous flow with a nonlinear elastic structure. The flow is described by the compressible Navier–Stokes equations written in the arbitrary Lagrangian–Eulerian (ALE) form. For the elastic deformation the St. Venant–Kirchhoff model is used. In the space discretization the discontinuous Galerkin finite element method (DGM) is applied both for the flow problem in a time-dependent domain and for the dynamic nonlinear elasticity system. We show that the DGM is applicable to the discretization of both problems. As a new result we particularly present the application of the DGM to the discretization of the dynamic nonlinear elasticity problem and the DGM solution of the fluid–structure interaction (FSI). The applicability of the developed technique is demonstrated by several numerical experiments. The main novelty of the paper is the application of the DGM to the FSI problem using the model of compressible flow coupled with nonlinear elasto-dynamic system. [ABSTRACT FROM AUTHOR]

Abstract: The paper is concerned with the simulation of viscous compressible flow in time dependent domains. The dependence on time of the domain occupied by the fluid is taken into account with the aid of the Arbitrary Lagrangian–Eulerian (ALE) formulation of the compressible Navier–Stokes equations. They are discretized by the discontinuous Galerkin finite element method using piecewise polynomial discontinuous approximations. The time discretization is based on a semi-implicit linearized scheme, which leads to the solution of a linear algebraic system on each time level. A suitable treatment of boundary conditions and shock capturing are used, allowing the solution of flow with a wide range of Mach numbers. The applicability of the developed method is demonstrated by computational results obtained for compressible viscous flow in a channel with moving walls and flow induced airfoil vibrations. [Copyright &y& Elsevier]