scholarly journals A reduced-order representation of the Poincaré-Steklov operator: an application to coupled multi-physics problems

2017 ◽  
Vol 111 (6) ◽  
pp. 581-600
Author(s):  
Matteo Aletti ◽  
Damiano Lombardi
Keyword(s):  
Reduced Order ◽  
Order Representation ◽  
Steklov Operator ◽  
Physics Problems

scholarly journals Model Order Reduction for convection dominated problems

2018 ◽  
Author(s):  
Harshit Bansal ◽  
Laura Iapichino ◽  
Stephan Rave ◽  
Wil Schilders ◽  
Nathan van de Wouw
Keyword(s):  
Order Reduction ◽  
Benchmark Problems ◽  
Reduced Basis ◽  
Order Model ◽  
Model Order ◽  
Reduced Order ◽  
Non Linear ◽  
Order Representation ◽  
Multi Phase ◽  
Convection Dominated

Model Order Reduction (MOR) of systems of non-linear(parameterized) Hyperbolic Partial Differential Equations (PDEs) is still an uncharted territory in the scientific community. Moving discontinuities are representative features of this class of problems and pose a major hindrance to obtain effective reduced-order model representations, since typically bases with high spatial frequency are needed to accurately capture these moving discontinuities. We will discuss a MOR framework to efficiently capture the travelling dynamics of such systems. The motivation of this work is to enable the usage of multi-phase hydraulic models, such as the Drift Flux Model (DFM) [2] in developing drilling automation strategies for real-time down-hole pressure management. The DFM is a system of multiscale non-linear PDEs, whose convective subset is conditionally hyperbolic. Convection dominated problems, such as the DFM, admit solutions, which possess a diagonal structure in space-time diagram and high solution variability. As a first step, we apply standard MOR approaches [4] to obtain a reduced-order representation of the DFM for a representative multi-phase shock tube test case. We capture the dynamics in an essentially non-oscillatory manner but we obtain a small dimensionality reduction. Since the dimension of the reduced model is still too large, we develop new techniques for deriving more efficient alternative reduced-order models for this class of problems. We invoke the idea of the method of freezing [1] and combine it with non-linear reduced basis approximations [3] to develop an efficient reduced-order model representation, which we demonstrate for several benchmark problems. These benchmark problems embody the challenges faced in the reduced-order representation of the DFM. However, the existing MOR framework [3] lacks consideration of boundary conditions and multiple fronts. The main novelty of this work is in investigating the performance of combined approach of Method of Freezing and reduced basis approximations in dealing with merging (discontinuous) wave-fronts. Finally, we present numerical experiments and discuss the efficacy of above mentioned approach in terms of computational speed up and computational accuracy compared with standard numerical techniques.

scholarly journals Reduced-order representation of turbulent jet flow and its noise source

2007 ◽  
Vol 16 ◽  
pp. 33-50 ◽  
Author(s):  
Elmar Gröschel ◽  
Wolfgang Schröder ◽  
Michael Schlegel ◽  
Jon Scouten ◽  
Bernd R. Noack ◽  
...  
Keyword(s):  
Noise Source ◽  
Jet Flow ◽  
Turbulent Jet ◽  
Reduced Order ◽  
Turbulent Jet Flow ◽  
Order Representation

scholarly journals Reduced-order representation of near-wall structures in the late transitional boundary layer

2014 ◽  
Vol 748 ◽  
pp. 278-301 ◽  
Author(s):  
Taraneh Sayadi ◽  
Peter J. Schmid ◽  
Joseph W. Nichols ◽  
Parviz Moin
Keyword(s):  
Shear Stress ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Reynolds Shear Stress ◽  
Low Frequency ◽  
Transition Process ◽  
Skin Friction Coefficient ◽  
Reduced Order ◽  
Wall Structures ◽  
Order Representation

AbstractDirect numerical simulations (DNS) of controlled H- and K-type transitions to turbulence in an $M = 0.2$ (where $M$ is the Mach number) nominally zero-pressure-gradient and spatially developing flat-plate boundary layer are considered. Sayadi, Hamman & Moin (J. Fluid Mech., vol. 724, 2013, pp. 480–509) showed that with the start of the transition process, the skin-friction profiles of these controlled transitions diverge abruptly from the laminar value and overshoot the turbulent estimation. The objective of this work is to identify the structures of dynamical importance throughout the transitional region. Dynamic mode decomposition (DMD) (Schmid, J. Fluid Mech., vol. 656, 2010, pp. 5–28) as an optimal phase-averaging process, together with triple decomposition (Reynolds & Hussain, J. Fluid Mech., vol. 54 (02), 1972, pp. 263–288), is employed to assess the contribution of each coherent structure to the total Reynolds shear stress. This analysis shows that low-frequency modes, corresponding to the legs of hairpin vortices, contribute most to the total Reynolds shear stress. The use of composite DMD of the vortical structures together with the skin-friction coefficient allows the assessment of the coupling between near-wall structures captured by the low-frequency modes and their contribution to the total skin-friction coefficient. We are able to show that the low-frequency modes provide an accurate estimate of the skin-friction coefficient through the transition process. This is of interest since large-eddy simulation (LES) of the same configuration fails to provide a good prediction of the rise to this overshoot. The reduced-order representation of the flow is used to compare the LES and the DNS results within this region. Application of this methodology to the LES of the H-type transition illustrates the effect of the grid resolution and the subgrid-scale model on the estimated shear stress of these low-frequency modes. The analysis shows that although the shapes and frequencies of the low-frequency modes are independent of the resolution, the amplitudes are underpredicted in the LES, resulting in underprediction of the Reynolds shear stress.

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