Discontinuous Galerkin method for the solution of compressible viscous flow

Title: Discontinuous Galerkin method for solving compressible viscous flow Author: Jan Česenek Department: Department of Numerical Mathematics Supervisor: prof. RNDr. Miloslav Feistauer, DrSc., dr.h.c., Department of Numerical Mathematics Abstract: The subject of this PhD thesis is the numerical simulation of the interaction of two-dimensional compressible viscous flow and a vibrating airfoil. We consider a solid airfoil with two degrees of freedom which can rotate around the elastic axis and oscillate in the vertical direction. The numerical simulation of this problem consist of the dis- continuous Galerkin finite element method solving Navier-Stokes equations coupled with a system of nonlinear ordinary differential equations describing the airfoil motion. The time-dependent domain is taken into account with the aid of the Arbitrary Lagrangian- Eulerian(ALE) formulation. Theoretical part of this paper is concerned with error esti- mates of the space-time discontinuous Galerkin method for scalar nonstationary equations with nonlinear convection and nonlinear diffusion. Keywords: convection-diffusion problems, discontinuous Galerkin method, interaction of a fluid with a vibrating airfoil, ALE metho