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Filtering in Large Eddy Simulation

Heslinga, O.L. (2010) Filtering in Large Eddy Simulation. Bachelor's Thesis, Mathematics.

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Abstract

We are all familiar with the concept of flow. Every day we feel the wind that blows and we see the water that moves. Observing the movement of fluids, one can immediately see that this is a very complex process. Whirls created by obstacles move fast and unpredictable and forces work in every direction causing the fluid to change its form constantly. For decades, mathematicians try to unfold the secrets behind the turbulent motion of fluids. Also nowadays, there is a wide range of applications involving flow of fluids. Think about aërodynamics, building dams and oil platforms. Solving these problems begins with the Navier-Stokes equations that form the base of this field of research. At first glance, just a set of equations containing mass and impulse balances combined with forces from the environment. However, in practice it is impossible to solve these equations exact and even with today's computers, solving by numerical simulation will ask too much calculating capacity. Every day engineers deal with problems too complex to solve with a computer. To still make an accurate simulation of turbulence, mathematicians came up with methods to simplify problems involving turbulent flow. By simulating only the larger structures in the flow and filtering out the smaller structures, computers are able to yield acceptable solutions. This form of simulating flow of fluids is called Large Eddy Simulation (LES). However, there is not one best way to perform LES. There are a lot of different features that can be adapted dependent to the problem that has to be solved. Think about the approximation used in the numerical simulation, the way the smaller structures are filtered out or the way these structures are being modelled. In this thesis, the focus will lie on the different ways to filter the solution. After a technical introduction to turbulent flow and LES in common, filtering will be discussed in more detail and different kinds of filters will be compared. These filters are first analyzed on a uniform grid. Later on, I choose a non- niform grid to study the consequences for a filter.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 07:44
Last Modified: 15 Feb 2018 07:44
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/9377

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