Finite Volume Methods
Finita volymmetoder

FMN015F, 7.5 högskolepoäng

Gäller från och med: Autumn 2014
Beslutad av: FN1/Anders Gustafsson
Datum för fastställande: 2015-03-15

Allmänna uppgifter

Avdelning: Numerical Analysis
Kurstyp: Gemensam kurs, avancerad nivå och forskarnivå
Kursen ges även på avancerad nivå med kurskod: NUMN14
Undervisningsspråk: English

Syfte

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.

Mål

Kunskap och förståelse

För godkänd kurs skall doktoranden demonstrate deep knowledge of mathematical and numerical difficulties regarding shock waves.

Färdighet och förmåga

För godkänd kurs skall doktoranden

• be able to independently choose, implement and use advanced computational methods for conservation laws.
• be able to report solutions and numerical simulations in written form.
• be able to judge the accuracy and relevance of numerical results

Kursinnehåll

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

Kurslitteratur

• Numerical Methods for Conservartion Laws.. ISBN 3764324643.
• Birken, P.: Numerical Methods for the Unsteady Navier-Stokes equations. Habilitation Thesis, University of Kassel.. 2012.

The course participants may download the second text from the course homepage.

Kursens undervisningsformer

Undervisningsformer: Föreläsningar, övningar

Kursens examination

Examinationsformer: Muntlig tentamen, inlämningsuppgifter
Betygsskala: Underkänd, godkänd
Examinator:

Antagningsuppgifter

Förutsatta förkunskaper: Vector analysis. Programming in Python or Matlab.

Övrig information

Contact person: Philipp Birken, philipp.birken@na.lu.se

Kurstillfällesinformation

Kontaktinformation och övrigt

Kursansvariga:
Hemsida: http://www.ctr.maths.lu.se/course/finitvol/