Informazioni sul corso

Lehrinhalte
Basic equations of incompressible fluid flow;
examples of exact solutions of the Navier-Stokes equations; i
ntroduction into the mathematical concept of symmetry;
the theory of Lie Groups;
Lies 1. and 2. fundamental theorem; dimensional analysis;
invariance of differential equations;
the Lie algorithm for determining symmetries;
invariant solutions of non-linear partial differential equations;
direct construction method of conservation laws in divergence form.

Literatur
Vorlesungsskript / lecture notes;  Bluman, Kumei: Symmetries and Differential equations, Springer Verlag, 1996; Stephani: Differentialgleichungen, Symmetrien und Lösungsmethoden, Spektrum Akademischer Verlag, 1994; Cantwell: Introduction to Symmetrie Analysis, Cambridge University Press, 2002;  Bluman, G.W., Cheviakov, A.F., and Anco, S.C.: Applications of Symmetry Methods to Partial Differential Equations. Applied Mathematical Sciences Vol. 168. Springer 2010.

Voraussetzungen
Basic knowledge of mathematics; basic knowledge of fluid mechanics.

Erwartete Teilnehmerzahl
15

Further Grading Information
Learning Outcomes
On successful completion of this module, students should be able to:
1. simplify the complexity of the Navier-Stokes equations for various simple flow problems and reach their exact solutions
2. apply the analytic theory, based on Lie symmetries, for solving ordinary and partial differential equations, specially for flow problems 
3. analyze the symmetries and invariances of given differential equations by means of the theory of Lie groups
4. development of potential local conservation laws of differential equations with the aid of the direct construction method.