# DGFEM for interaction of fluids and nonlinear elasticity

## Main Article Content

## Abstract

This paper is concerned with the numerical simulation of the interaction of compressible viscous flow with elastic structures. The flow is described by the compressible Navier-Stokes equations written in the arbitrary Lagrangian-Eulerian (ALE) form. For the elastic deformation we use 2D linear elasticity and nonlinear St.~Venant-Kirchhoff and neo-Hookean models. The discretization of both flow problem and elasticity problem is realized by the discontinuous Galerkin finite element method (DGFEM). The main attention is paid to testing the DGFEM applied to the solution of elasticity problems. Then we present an example of the fluid-structure interaction (FSI). The applicability of the developed technique is demonstrated by several numerical experiments.

## Article Details

How to Cite

Feistauer, M., Hadrava, M., Kosík, A., & Horáček, J.
(2016).
DGFEM for interaction of fluids and nonlinear elasticity.

*Proceedings Of The Conference Algoritmy,*, 74-83. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/396/313
Section

Articles

## References

[1] J. Cesenek, M. Feistauer and A. Kosík, DGFEM for the analysis of airfoil vibrations induced by compressible flow, Z. Angew. Math. Mech., vol 93 (2013), No. 6-7, 387 402.

[2] P. G. Ciarlet, Mathematical Elasticity, Volume I, Three-Dimensional Elasticity, Volume 20 of Studies in Mathematics and its Applications, Elsevier Science Publishers B.V., Amsterdam, 1988.

[3] V. Dolejší and M. Feistauer, Discontinuous Galerkin Method, Analysis and Applications to Compressible Flow, Volume 48 of Springer Series in Computational Mathematics, Springer, Cham, 2015.

[4] M. Feistauer, J. Horáček, V. Kučera and J. Prokopová, On numerical solution of com- pressible flow in time-dependent domains, Mathematica Bohemica, 137 (2011), 1-16.

[5] T. Nomura and T. J. R. Hughes, An arbitrary Lagrangian-Eulerian finite element method for interaction of flow and a rigid body, Comput. Methods Appl. Mech. Engrg., 95 (1992), 115-138.

[6] I.R. Titze, Principles of Voice Production, National Centre for Voice and Speech, Iowa City, 2000.

[7] S. Turek, J. Hron, Proposal for numerical benchmarking of fluidstructure interaction between an elastic object and laminar incompressible flow, in: H. J. Bungartz, M. Sch ̈ afer (Eds.), Fluid-Structure Interaction: Modelling, Simulation, Optimisation, Springer, Berlin, 2006, 371-385.

[2] P. G. Ciarlet, Mathematical Elasticity, Volume I, Three-Dimensional Elasticity, Volume 20 of Studies in Mathematics and its Applications, Elsevier Science Publishers B.V., Amsterdam, 1988.

[3] V. Dolejší and M. Feistauer, Discontinuous Galerkin Method, Analysis and Applications to Compressible Flow, Volume 48 of Springer Series in Computational Mathematics, Springer, Cham, 2015.

[4] M. Feistauer, J. Horáček, V. Kučera and J. Prokopová, On numerical solution of com- pressible flow in time-dependent domains, Mathematica Bohemica, 137 (2011), 1-16.

[5] T. Nomura and T. J. R. Hughes, An arbitrary Lagrangian-Eulerian finite element method for interaction of flow and a rigid body, Comput. Methods Appl. Mech. Engrg., 95 (1992), 115-138.

[6] I.R. Titze, Principles of Voice Production, National Centre for Voice and Speech, Iowa City, 2000.

[7] S. Turek, J. Hron, Proposal for numerical benchmarking of fluidstructure interaction between an elastic object and laminar incompressible flow, in: H. J. Bungartz, M. Sch ̈ afer (Eds.), Fluid-Structure Interaction: Modelling, Simulation, Optimisation, Springer, Berlin, 2006, 371-385.