Finite volume - space-time discontinuous Galerkin method for the numerical simulation of compressible turbulent flow in time dependent domains

The article is concerned with the numerical simulation of the compressible turbulent flow in time dependent domains. The mathematical model of flow is represented by the system of non-stationary Reynolds- Averaged Navier-Stokes (RANS) equations. The motion of the domain occupied by the fluid is taken into account with the aid of the ALE (Arbitrary Lagrangian-Eulerian) formulation of the RANS equations. This RANS system is equipped with two-equation k − ω turbulence model. These two systems of equations are solved separately. Discretization of the RANS system is carried out by the space-time discontinuous Galerkin method which is based on piecewise polynomial discontinuous approximation of the sought solution in space and in time. Discretization of the two-equation k − ω turbulence model is carried out by the implicit finite volume method, which is based on piecewise constant approximation of the sought solution. We present some numerical experiments to demonstrate the applicability of the method using own-developed code

The influence of penalization inlet boundary condition on the stability boundary

Grant No. GA19-04477S of Czech Science Foundation and by Grant No. SGS19/154/OHK2/3T/12 of the CTU in Pragu

On algebraic flux corrections for finite element approximation of transport phenomena

CZ.02.1.01/0.0/0.0/16 019/000082

On mathematical models of airflow in a glottal channel model periodically closed by flow induced vocal folds vibration

Czech Science Foundation under the Grant No. 19 - 04477

On application of finite element method for approximation of 3D flow problems

This paper is interested to the interactions of the incompressible flow with a flexibly supported airfoil. The bending and the torsion modes are considered. The problem is mathematically described. The numerical method is based on the finite element method. A combination of the streamline-upwind/Petrov-Galerkin and pressure stabilizing/Petrov-Galerkin method is used for the stabilization of the finite element method. The numerical results for a three-dimensional problem of flow over an airfoil are shown

On mathematical modelling of gust response using the finite element method

In this paper the numerical approximation of aeroelastic response to sudden gust is presented. The fully coupled formulation of two dimensional incompressible viscous fluid flow over a flexibly supported structure is used. The flow is modelled with the system of Navier-Stokes equations written in Arbitrary Lagrangian-Eulerian form and coupled with system of ordinary differential equations describing the airfoil vibrations with two degrees of freedom. The Navier-Stokes equations are spatially discretized by the fully stabilized finite element method. The numerical results are shown

On modelling and simulation of flow in the vocal tract with consideration of the glottis closure

Czech Science Foundation under the Grant No. 19 - 07744

On approximation of an aeroelastic problem in post-critical regimes

This paper focused on the mathematical modelling and the numerical approximation of interactions of a simplified problem of the two-dimensional flow and flexibly supported airfoil section with control section. The flow is modelled with the aid of the incompressible Navier-Stokes equations and for the approximation the stabilized finite element method is used. The structure motion is described with the aid of nonlinear ordinary differential equations. The time-dependent computational domain is taken into account by the Arbitrary Lagrangian-Eulerian method

Finite element method application for fluid structure interactions: Mathematical background and implementation

This work was supported by the Czech Science Foundation under the Grant No. 16 - 01246S.In this paper the mathematical modelling of fluid-structure interaction problems is addressed particularly with the interest paid to the biomechanics of human voice. The attention is paid to the precise approximation of the fluid flow, particularly in the glottal part, with the aid of the numerical approximation of the Navier?Stokes equations. This problem is even more complicated in the context of the voice creation process, e.g., by the glottal gap closing or by the presence of the contact problem. In this case one need to take into account not only a significant mesh deformation but also the influence of the prescribed artificial inlet/outlet boundary conditions