EP8408 - High Order Methods in Fluid Dynamics

About

Examination arrangement

Examination arrangement: Written examination
Grade: Passed/Failed

Evaluation form Weighting Duration Examination aids Grade deviation
Written examination 100/100 4 hours D

Course content

The course is taught every second year. First Autumn2016 and next 2018. The PhD course will give an overview over high order methods in fluid dynamics. Since high order methods are much more efficient than low order methods for high accuracy requirements, high order methods have frequently been used in direct numerical and large eddy simulation of turbulence, computational aeroacoustics, etc. In the course, high order finite difference, element and volume methods as well as spectral and spectral element methods will be outlined. Dissipation and dispersion errors will be analyzed, and the effect of low pass filters will be investigated. Optimized high order finite difference schemes with low dissipation and dispersion errors will be derived. Boundary stencils will be constructed, which guarantee not only high accuracy but also strict stability. As those schemes are based on the discrete analogue of integration by parts, they exhibit a similar energy growth as the continuous problem. That property is important for accurate simulations of viscous and inviscid flows and of waves. The pros and cons of different high order time discretizations will be discussed.

The implementation of boundary conditions in high order methods will be outlined. We shall focus on absorbing boundary conditions (ABC) for wave problems, namely Engquist-Majda ABC, ABC based on asymptotic expansions, perfectly matched layer method, buffer layer / sponge zone method.

Applications to the compressible Euler equations and to the compressible and incompressible Navier-Stokes equations will illustrate the advantages of using high order methods for fluid flow simulations.

Learning outcome

The participants will get an overview over high order methods in fluid dynamics and insight into the application of high order finite difference methods to compressible and incompressible flow simulations.

Knowledge:
- After completion of this course, the student will have knowledge on:
• Overview over high order finite difference, element and volume methods as well as spectral and spectral element methods.
• Dissipation and dispersion errors as well as the effect of low pass filters.
• Optimized high order finite difference schemes with low dissipation and dispersion errors.
• Boundary stencils, which guarantee not only high accuracy but also strict stability.
• The energy method for continuous and discrete problems.
• High order time discretizations.
• The implementation of boundary conditions in high order methods.
• Absorbing boundary conditions (ABC) for wave problems, namely Engquist-Majda ABC, ABC based on asymptotic expansions, perfectly matched layer method, buffer layer / sponge zone method.
• Applications to the compressible Euler equations and to the compressible and incompressible Navier-Stokes equations.


Skills:
- After completion of this course, the student will have skills on:
• Practical use and programming of high order difference methods in fluid dynamics.
• Checking and assessing the accuracy of numerical results with high order methods.
• Consistency analysis and von Neumann stability analysis for high order difference methods.
• Using the energy method for well-posedness analysis and stability analysis.
• Derivation and use of absorbing boundary conditions.
• Implementation of Dirichlet and Neumann boundary conditions into high order difference methods.
• Using high order difference methods for the linear Euler equations in acoustics.

General competence:
- After completion of this course, the student will have general competence on:
• Numerical solution of practical fluid flow problems with high order difference methods.
• Analysis of high order difference methods with different boundary conditions.

Learning methods and activities

Lectures and written exercises.
If there is a re-sit examination, the examination form may be changed from written to oral. To pass the course a score of at least 70 percent is required.

Required previous knowledge

Course TEP4165 Computational Heat and Fluid Flow or an equivalent CFD course.

Course materials

Bertil Gustafsson: "High Order Difference Methods for Time Dependent PDE." Springer, Berlin, 2008.

Timetable

Detailed timetable

Examination

Examination arrangement: Written examination

Term Statuskode Evaluation form Weighting Examination aids Date Time Room *
Autumn ORD Written examination 100/100 D 2016-12-06 09:00 C
Spring ORD Written examination 100/100 D
  • * The location (room) for a written examination is published 3 days before examination date.
If more than one room is listed, you will find your room at Studentweb.