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Instructors: Dr. Claus Rüdiger Goetz
Event type:
Lecture
Displayed in timetable as:
M-WR-V
Hours per week:
2
Language of instruction:
English
Min. | Max. participants:
- | -
Comments/contents:
Hyperbolic conservation laws are first-order partial differential equations in space and time that arise in a wide range of applications, ranging from gas and fluid dynamics to the modelling of traffic flow or elasticity. From a mathematical point of view the outstanding property of nonlinear hyperbolic conservation laws is that solutions may develop discontinuities in finite time, even for arbitrarily smooth initial data.
In this class we will discuss advanced numerical methods for the solution of hyperbolic conservation laws, in particular for nonlinear system, such as the Euler equations or shallow water equations. This will also require the study of some of their analytical properties.
Topics covered in this class will include:
- the Godunov scheme
- slope- and flux-limiters
- the Riemann problem
- approximate Riemann solvers
- high-order WENO reconstruction
- generalized Riemann problems
The class will be largely self-contained, but some familiarity with
- partial differential equations
- finite volume methods
is highly recommended.
Learning objectives:
The goal of this class is to understand the key analytical properties of hyperbolic conservation laws, how they translate to state-of-the-art numerical methods, and how to implement those methods.
Didactic concept:
There will be one 90 min lecture each week, accompanied by exercise classes every other week. Exercises will be solved in groups. There will be coding exercises.
Literature:
There will be a script. Additional references and material will be provided in the lecture.
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