Masterproef T705 : Model order reduction and linearisation for the simulation of wind farms
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Begeleiding:
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Onderzoeksgroep:
Numerieke Approximatie en Lineaire Algebra Groep
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Context:
There is currently a master’s thesis on-going on model order reduction for optimization of the controls of windturbines in a wind farm. This thesis studied the use of Proper Orthogonal Decompositions (POD) in order to reduce the size of the model from a few million to a few hundred or thousand. We now want to investigate a new but controversial idea: approximate a nonlinear system by a small scale linear system.
Doel:
In a follow-up thesis we want to study other reduced models based on the so-called Carleman linearisation. We will analyse for which type of flows such Carleman linearisation leads to a reduced model. It is expected that this is possible for laminar flow and much more difficult or impossible for turbulent flows. |
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Uitwerking:
The student starts reading papers and the master thesis that was carried out this year. The software developed in this thesis can be used to generate the differential equations and POD reduced models. Those are a good starting point. The main part of the thesis is to apply the Carleman linearisation or variations to the Navier-Stokes equations. It is expected that near a steady state the Carleman linearisation is leading to a very good approximation of the nonlinear model. This will be verified experimentally. Away from a steady state, we will have to modify the classical Carleman linearisation by interpolating the solution for a small number of time steps. |
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Profiel:
The work involves some theory and some practical implementations to test the different ideas. Knowledge of computational fluid dynamics (CFD) is not required but may be helpful for understanding the context. Matlab can be used initially for small tests, but in the end, for realistic computations, a compilable language should be used. Deze masterproef is voor 1 or 2 studenten. |