Discontinuous Galerkin method for problems in time-depend domains – theory and applications

Abstract: Most of the theoretical mathematical results on the solvability and numerical analysis of nonstationary partial differential equations are obtained under the assumption that a space domain is independent of time. However, problems in time-dependent domains are important in a number of areas of science and technology. This is particularly the case of fluid-structure interaction problems, when the flow is solved in a domain deformed due to the coupling with an elastic structure. There are various approaches to the solution of problems in time-dependent domains, a very popular technique is the arbitrary Lagrangian-Eulerian (ALE) method. In this talk we present an ALE version of the space-time discontinuous Galerkin method, which is based on piecewise polynomial approximations over finite element meshes, in general discontinuous on interfaces between neighbouring elements. We show that the proposed method is numerically unconditionally stable and demonstrate its robustness on a numerical solution of the nonlinear elasticity benchmark problem. The developed method is also applied to the numerical simulation of air flow in a simplified model of human vocal tract and flow induced vocal folds vibrations.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)