Diploma and Master Theses (authored and supervised):
"Pressure Robust Discretizations for Navier Stokes Equations: Divergence-free Reconstruction for Taylor-Hood Elements and High Order Hybrid Discontinuous Galerkin Methods";
Supervisor: J. Schöberl, S. Braun;
Institut für Analysis und Scientific Computing,
final examination: 2016-04-25.
This thesis focuses on a well-known issue of discretization techniques for solving the incompressible Navier Stokes equations. Due to a weak treatment of the incompressibility constraint there are different disadvantages that appear, which can have a major impact on the convergence and physical behaviour of the solutions. First we approximate the
equations with a well-known pair of elements and introduce an operator that creates a reconstruction into a proper space to fix the mentioned problems.
Afterwards we use an H (div) conforming method that already handles the incompressibility constraint in a proper way. For a stable high order approximation an estimation for the saddlepoint structure of the Stokes equations is needed, known as the Ladyschenskaja-Babuˇska-Brezzi (LBB) condition. The independency of the estimation from the order of the polynomial degree is shown in this thesis. For that we introduce an H 2-stable extension that preserves polynomials.
All operators and schemes are implemented based on the finite element library Netgen/NGSolve and tested with proper examples.
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.