Valid from: Autumn 2014
Decided by: FN1/Anders Gustafsson
Date of establishment: 2015-03-15
Division: Numerical Analysis
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: NUMN14
Teaching language: English
Finite Volume methods are the standard numerical methods for the solution of conservation laws, which represent fundamental laws of physics. Of particular importance is the use of the latter to model fluid flows in the form of parabolic and hyperbolic partial differential equations. The course explains basic pitfalls of numerical methods for these equations and how to arrive at stable and convergent finite volume methods of first order. The course is necessary for further studies within numerical analysis and also useful for students within applied disciplins where conservation laws are used.
Knowledge and Understanding
For a passing grade the doctoral student must demonstrate deep knowledge of mathematical and numerical difficulties regarding shock waves.
Competences and Skills
For a passing grade the doctoral student must
Conservation Laws, Reynolds' Transport theorem, Navier-Stokes equations Upwind methods and central discretizations Stability and the Courant-Friedrichs-Lewys (CFL) condition The theorem of Lax Wendroff Characteristics, Linear Systems Nonlinear systems, Roe's method Uniqueness, Entropy solutions, Entropy condition Finite Volume methods in multiple dimensions Boundary conditions Time Integration Higher Order, Theorem of Godunov, Discontinuous Galerkin (DG) Methods Quadrature, DG-Spectral Element Methods Stability of DG methods, Time Integration aspects
The course participants may download the second text from the course homepage.
Types of instruction: Lectures, exercises
Examination formats: Oral exam, written assignments
Grading scale: Failed, pass
Assumed prior knowledge: Vector analysis. Programming in Python or Matlab.
Contact person: Philipp Birken, email@example.com
Web page: http://www.ctr.maths.lu.se/course/finitvol/