Course - High Order Methods in Fluid Dynamics - EP8408
High Order Methods in Fluid Dynamics
About
About the course
Course content
The course is taught every second year, next time Autumn 2010. 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 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. 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 and 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 flow simulations.
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.
Recommended previous knowledge
The subject requires good basic knowledge in computational fluid dynamics (CFD).
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.
Subject areas
- Numerical Mathematics
- Fluid Mechanics
- Technological subjects