The paper deals with numerical simulation of a compressible flow in timedependent 2D domains with a special interest in medical applications to airflow in the human vocal tract. The mathematical model of this process is described by the compressible Navier-Stokes equations. For the treatment of the time-dependent domain, the arbitrary Lagrangian-Eulerian (ALE) method is used. The discontinuous ...

Abstract. This work is concerned with the simulation of compressible flow in time dependent domains. We present an ALE (Arbitrary Lagrangian-Eulerian) formulation of the Navier-Stokes equations describing compressible flow, discretize them in space by the discontinous Galerkin method and introduce a semi-implicit linearized time stepping for the numerical solution of the complete problem. We pr...

We consider a monolithic scheme for fluid–structure interaction problems involving an incompressible quasi-Newtonian fluid. The monolithic formulation is obtained using the Arbitrary Lagrangian Eulerian (ALE) method with matching conditions at the fluid–structure interface. The stability and error analysis are performed for the finite element approximation. Finally, some numerical experiments t...

We examine several aspects of the formulation of M(atrix)-Theory on ALE spaces. We argue for the existence of massless vector multiplets in the resolved An−1 spaces, as required by enhanced gauge symmetry in M-Theory, and that these states might have the correct gravitational interactions. We propose a matrix model which describes M-Theory on an ALE space in the presence of wrapped membranes. W...

Finite element method (FEM) was used for numerical simulation of the airflow field in a simplified model of the human vocal tract for vowel /a:/ with prescribed periodic oscillations of the vocal folds. The viscous fluid is modeled by 2D compressible Navier-Stokes equations in Arbitrary LagrangianEulerian (ALE) formulation and considering the turbulence. The computed flow field pattern is compa...

We study the numerical approximation of a flow problem governed by a viscoelastic model coupled with a one-dimensional elastic structure equation. A variational formulation for flow equations is developed based on the Arbitrary Lagrangian-Eulerian (ALE) method and stability of the time discretized system is investigated. For decoupled numerical algorithms we consider both an explicit scheme of ...

We present a new approach for multi-material Arbitrary Lagrangian-Eulerian (ALE) hydrodynamics simulations based on high-order finite elements posed on high-order curvilinear meshes. The method builds on and extends our previous work in the Lagrangian [1] and remap [2] phases of ALE, and depends critically on a functional perspective that enables sub-zonal physics and material modeling [3]. Cur...

Galilean invariance is one of the key requirements of many physical models adopted in theoretical and computational mechanics. Spurred by recent research developments in shock hydrodynamics computations [13], a detailed analysis on the principle of Galilean invariance in the context of SUPG operators is presented. It was observed in [13] that lack of Galilean invariance can yield catastrophic i...