Abstract
Original language  English 

Awarding Institution 

Supervisors/Advisors 

Thesis sponsors  
Award date  28 Sep 2007 
Place of Publication  Enschede 
Publisher  
Print ISBNs  9789036525459 
Publication status  Published  28 Sep 2007 
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Keywords
 METIS241960
 EWI11168
 IR57928
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Research output: Thesis › PhD Thesis  Research UT, graduation UT
TY  THES
T1  Discontinuous Galerkin Finite Element Methods for the NavierStokes Equations in Entropy Variable Formulation
AU  Pesch, L.
PY  2007/9/28
Y1  2007/9/28
N2  Many numerical methods for fluid dynamics are suitable only for a single, idealized type of fluid. Most prominently, algorithms for compressible flow are often tailored to ideal gases and another class of schemes is designed for incompressible media. This dissertation targets a numerical method for the simulation of the flow of fluids with differing thermodynamical properties, in particular both compressible and incompressible fluids. By considering the NavierStokes equations in terms of certain generalized variable sets, the singularity of the incompressible limit, which arises when using conservation variables, can be avoided. Especially entropy variables, which stem from symmetrization theory, can ensure desirable properties like the fulfillment of the second law of thermodynamics. To obtain a discretization that allows local adaptation and high geometric flexibility, a spacetime discontinuous Galerkin finite element method is developed. Particular attention is paid to the examination which components of the numerical method have to be adapted when using specific thermodynamical models. Numerical results for a diverse range of compressible and incompressible test cases underline the applicability of the method for various fluids and conditions. Apart from the numerical algorithms, the project also involved the further development of the objectoriented generalpurpose discontinuous Galerkin finite element software framework hpGEM. This thesis presents aspects of its philosophy and design, and discusses examples of how the components can be applied. The formulation in terms of general sets of variables, a mathematical method that accommodates geometric flexibility and adaptivity, and a software environment for the implementation of numerical methods are important parts for the construction of finite element methods for gasliquid multiphase flows.
AB  Many numerical methods for fluid dynamics are suitable only for a single, idealized type of fluid. Most prominently, algorithms for compressible flow are often tailored to ideal gases and another class of schemes is designed for incompressible media. This dissertation targets a numerical method for the simulation of the flow of fluids with differing thermodynamical properties, in particular both compressible and incompressible fluids. By considering the NavierStokes equations in terms of certain generalized variable sets, the singularity of the incompressible limit, which arises when using conservation variables, can be avoided. Especially entropy variables, which stem from symmetrization theory, can ensure desirable properties like the fulfillment of the second law of thermodynamics. To obtain a discretization that allows local adaptation and high geometric flexibility, a spacetime discontinuous Galerkin finite element method is developed. Particular attention is paid to the examination which components of the numerical method have to be adapted when using specific thermodynamical models. Numerical results for a diverse range of compressible and incompressible test cases underline the applicability of the method for various fluids and conditions. Apart from the numerical algorithms, the project also involved the further development of the objectoriented generalpurpose discontinuous Galerkin finite element software framework hpGEM. This thesis presents aspects of its philosophy and design, and discusses examples of how the components can be applied. The formulation in terms of general sets of variables, a mathematical method that accommodates geometric flexibility and adaptivity, and a software environment for the implementation of numerical methods are important parts for the construction of finite element methods for gasliquid multiphase flows.
KW  METIS241960
KW  EWI11168
KW  IR57928
M3  PhD Thesis  Research UT, graduation UT
SN  9789036525459
PB  University of Twente
CY  Enschede
ER 