SC²S Colloquium - February 9, 2018
|Date:||February 9, 2018|
|Time:||3:00 pm, s.t.|
Lisa Scheller: Finite volume and discontinuous Galerkin methods for hyperbolic partial differential equations
This bachelor’s thesis gives an overview over hyperbolic partial differential equations, especially the shallow water equations. Several numerical methods for solving these kind of problems are described and compared, focusing on finite volume methods and discontinuous Galerkin methods. Since for those methods numerical flux functions are used, some of them are also explained. An analytic solution for dam break problems is developed for later error computing and convergence analysis. The implementation of both a finite volume solver, as well as a discontinuous Galerkin solver, is described in detail, also which scenarios were used and what results were computed. This is used to compare finite volume and discontinuous Galerkin approaches. After that, the error of the methods is computed and the order of convergence of the method determined. The methods are then compared in regard to this.