Goal-Oriented, Reduced-Order Modeling of the Incompressible Navier-Stokes Equations
Application to a 2D transitional boundary layer
P.H.L. Blom (TU Delft - Aerospace Engineering)
Seven J. Hulshoff – Mentor (TU Delft - Aerodynamics)
J. Casacuberta – Graduation committee member (TU Delft - Aerodynamics)
Marios Kotsonis – Graduation committee member (TU Delft - Aerodynamics)
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Abstract
Research into constructing reduced-order models (ROM) to reduce computational cost or to interpret complex datasets from numerical or experimental sources has steadily been gaining popularity over the past few years. Many methods currently exist to construct ROMs. The proper orthogonal decomposition (POD) is one of the most widely adopted methods used for these purposes in the field of fluid dynamics. The POD modes favor high-energy structures due to the formulation of the POD however. This may result in an inaccurate ROM, as it might be possible that dynamically relevant, yet low-energy structures are truncated in favor of higher-energy structures. In recent years, an alternative goal-oriented method has been proposed. This goal-oriented method not only has less limits on the goal function that is optimally represented relative to thePOD, the resulting reconstruction of the flow field is model constrained as well. Both these properties are conjectured to lead to more dynamically relevant modes. This goal-oriented, reduced-order modeling (GOROM) technique has been formalized for the advection, Burger’s and incompressible Navier-Stokes equations in 1D and the Stokes equations in 2D, all with homogeneous boundary conditions. This work extends the formulation to the 3D incompressible Navier-Stokes equations with inhomogeneous boundary conditions and provides a parallel implementation. The method is applied to a DNS dataset of a 2D transitional boundary layer with and without a forward-facing step present and compared to the performance of the POD. It is found that the GOROM modes provide a basis which is numerically more accurate than the POD modes for most cases, yet do not provide additional insight into the flow physics. The results presented nevertheless show promise for further applications to construct more accurate and goal-oriented ROMs with the GOROM technique, especially for problems with nonlinear interactions and nonlinear goal functions.