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Wall-based reduced order modelling

Wall-based reduced order modelling
Wall-based reduced order modelling
In this work we propose a novel approach to model order reduction for incompressible fluid flows that focuses on the spatio-temporal description of the stresses on the surface of a body, i.e. of the wall shear stress and of the wall pressure. The spatial representation of these two variables is given by a compact set of “wall basis functions”, i.e. elementary basis functions defined on the wall. In this paper, these are derived using the well-known Proper Orthogonal Decomposition, to represent optimally the fluctuation energy of the pressure and shear stress. On the other hand, the functional structure of the dynamic model is derived from first principles using the vorticity form of the Navier-Stokes equations, yielding a set of nonlinear ordinary differential equations for the time varying amplitudes of the wall shear stress basis functions. Coefficients of this model are then identified from simulation data. To complete the system, we show that the surface pressure distribution, i.e. the time-varying amplitudes of the wall pressure basis functions, can be derived from a quadratic model of the wall shear stress temporal coefficients, stemming from the Poisson equation for the pressure. This further step is crucial for the correct representation of the aerodynamic forces. As a paradigmatic example, we present our approach for the modelling of the free dynamics of the separated flow around a circular cylinder in the laminar regime, at Re = 200. Further implications and potentialities of the proposed approach are discussed.
0271-2091
511-535
Lasagna, Davide
0340a87f-f323-40fb-be9f-6de101486b24
Tutty, Owen
c9ba0b98-4790-4a72-b5b7-09c1c6e20375
Lasagna, Davide
0340a87f-f323-40fb-be9f-6de101486b24
Tutty, Owen
c9ba0b98-4790-4a72-b5b7-09c1c6e20375

Lasagna, Davide and Tutty, Owen (2016) Wall-based reduced order modelling. International Journal for Numerical Methods in Fluids, 80 (9), 511-535. (doi:10.1002/fld.4163).

Record type: Article

Abstract

In this work we propose a novel approach to model order reduction for incompressible fluid flows that focuses on the spatio-temporal description of the stresses on the surface of a body, i.e. of the wall shear stress and of the wall pressure. The spatial representation of these two variables is given by a compact set of “wall basis functions”, i.e. elementary basis functions defined on the wall. In this paper, these are derived using the well-known Proper Orthogonal Decomposition, to represent optimally the fluctuation energy of the pressure and shear stress. On the other hand, the functional structure of the dynamic model is derived from first principles using the vorticity form of the Navier-Stokes equations, yielding a set of nonlinear ordinary differential equations for the time varying amplitudes of the wall shear stress basis functions. Coefficients of this model are then identified from simulation data. To complete the system, we show that the surface pressure distribution, i.e. the time-varying amplitudes of the wall pressure basis functions, can be derived from a quadratic model of the wall shear stress temporal coefficients, stemming from the Poisson equation for the pressure. This further step is crucial for the correct representation of the aerodynamic forces. As a paradigmatic example, we present our approach for the modelling of the free dynamics of the separated flow around a circular cylinder in the laminar regime, at Re = 200. Further implications and potentialities of the proposed approach are discussed.

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More information

Accepted/In Press date: 20 August 2015
e-pub ahead of print date: 1 October 2015
Published date: 30 March 2016
Organisations: Aeronautics, Astronautics & Comp. Eng

Identifiers

Local EPrints ID: 384135
URI: https://eprints.soton.ac.uk/id/eprint/384135
ISSN: 0271-2091
PURE UUID: ba6086f7-20ec-462a-9ca3-02afd57d68c4
ORCID for Davide Lasagna: ORCID iD orcid.org/0000-0002-6501-6041

Catalogue record

Date deposited: 15 Dec 2015 13:32
Last modified: 10 Sep 2019 00:35

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