Algorithms for Solving the Euler and Navier-Stokes Equations

Course content

Systematic extension of the basic knowledge acquired in the bachelor's degree programme in mathematics and expansion of knowledge and expertise in additional areas of mathematics, gain an understanding of the complex links between the different areas of applied and pure mathematics, studying theories and mastering their complex methods and studying in-depth mathematical applications also through project-type examples, realization of algorithms introduced in numerical mathematics, get to know data structures required for meshing strategies, differentiation of discretized partial differential and integral equations and realization of their representation in programming languages

Content
The lecture is about algorithms suited to approximate solutions of the Euler and Navier-Stokes equations. Starting with well-known discretization schemes (such as finite-volume methods) the focus of the lecture is the design of smoothers for nonlinear multigrid methods. These smoothers are based on the idea of implicit Runge-Kutta methods. To realize these methods necessary requirements, for example differentiation of discretized governing equations, structure of derivative matrices as well as iterative methods for efficiently solving the linear systems, are discussed. Finally, different variants of these methods are compared and their advantages and disadvantages are discussed.