Conservative Model Order Reduction for Fluid Flow

Afkham, Babak Maboudi; Ripamonti, Nicolò; Wang, Qian; Hesthaven, Jan S.

doi:10.1007/978-3-030-48721-8_4

Cited by 12 publications

(9 citation statements)

References 37 publications

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“…The preservation of secondary conservation is also of importance in numerical schemes [40] and its importance in ROM stability has been emphasized by Afkham et al [41]. Both the FOM and ROM solutions are based on the primary conservation laws, but secondary conservation (kinetic energy, k, and entropy, s) is evaluated by means of the following, Kinetic Energy:…”

Section: Conservation Law Preservationmentioning

confidence: 99%

Investigations and Improvement of Robustness of Reduced-Order Models of Reacting Flow

2019

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The impact of chemical reactions on the robustness and accuracy of projectionbased Reduced-Order Models (ROMs) of fluid flows is investigated. Both Galerkin and Least-Squares Petrov Galerkin ROMs are shown to be less robust in reacting flows as compared to non-reacting flows. In particular, reacting flow ROMs show a strong sensitivity to the resolution and are often unstable. To identify the main underlying causes, a representative problem that contains the essential physics encountered in typical combustion dynamics problems is chosen. Comparisons with non-reacting solutions are used to assess the impact of reactions. Investigations are focused on three potential areas of significance: 1) preservation of conservation laws; 2) loss of dissipation; and 3) existence of unphysical local phenomena. Results indicate that conservation is relatively well-controlled and the global dissipation in the ROMs is actually larger than that in the underlying CFD solutions. Spurious local phenomena are, however, highly deleterious. Specifically, the steep temperature gradients that characterize combustion can lead to oscillations in local temperatures even in the absence of reactions. Representative calculations with physics-based temperature constraints verify that eliminating such excursions results in considerable improvement in both stability and future-state prediction capability.

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Section: Conservation Law Preservationmentioning

confidence: 99%

Investigations and Improvement of Robustness of Reduced-Order Models of Reacting Flow

2019

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“…Ahmed et al 48 present a comprehensive review of the state of the art in closure modeling for projection-based ROMs. It has been shown that maintaining the conservation properties of the governing equations is critical in ROM development 49 . A method demonstrated by 50 generates stable non-linear ROMs by minimizing the least-squares residual of the projected solution, yielding in a symmetrized and linearly stable ROM.…”

Section: Projection-based Reduced-order Modelingmentioning

confidence: 99%

Large-eddy simulation and challenges for projection-based reduced-order modeling of a gas turbine model combustor

Arnold-Medabalimi

Huang

Duraisamy

2022

International Journal of Spray and Combustion Dynamics

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Computationally efficient modeling of gas turbine combustion is challenging due to the chaotic multi-scale physics and the complex non-linear interactions between acoustic, hydrodynamic, and chemical processes. A large-eddy simulation, referred to as the full order model (FOM), is performed for a gas turbine model combustor with turbulent combustion effects modeled using a flamelet-based method. Modal analysis reveals a high degree of correlation with averaged and instantaneous high-frequency particle image velocimetry fields. The dynamics of the precessing vortex core is quantitatively characterized using dynamic mode decomposition. The governing equations of the FOM are projected onto a low-dimensional linear manifold to construct a reduced-order model (ROM). A discretely-consistent least squares projection is used to guarantee global stability. The ROM provides an accurate reconstruction of the combustion dynamics within the training region, but faces a significant challenge in future state predictions. This limitation is mainly due to the increased projection error, which in turn is a direct consequence of the highly chaotic nature of the flow field, involving a wide range of dispersed coherent structures. This shortcoming is overcome using an adaptive basis method which yields accurate predictions of dynamics beyond the training region consistent with the FOM. Formal projection-based ROMs have not been applied to a problem of this scale and complexity, and achieving accurate and efficient ROMs is a grand challenge problem. A production-ready ROM method will significantly decrease the computational cost of the flame dynamics as well as the portability of this prediction to smaller-scale computers.

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“…We begin by applying sparse sampling and interpolation to the non-linear equation residual r in Eq. 34 qn…”

Section: Hyper-reductionmentioning

confidence: 99%

“…While these methods can enable stable ROMs, they can compromise the conservative properties of the governing equations during the model reduction procedure. Afkham et al [34] highlighted the importance of preserving the conservative form of the governing equations in ROM development.…”

Section: Introductionmentioning

confidence: 99%

Model Reduction for Multi-Scale Transport Problems using Model-form Preserving Least-Squares Projections with Variable Transformation

Huang¹,

Wentland²,

Duraisamy³

et al. 2020

Preprint

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A projection-based formulation is presented for non-linear model reduction of problems with extreme scale disparity. The approach allows for the selection of an arbitrary, but complete, set of solution variables while preserving the conservative form of the governing equations. Least-squares-based minimization is leveraged to guarantee symmetrization and discrete consistency with the full-order model (FOM) at the sub-iteration level. Two levels of scaling are used to achieve the conditioning required to effectively handle problems with extremely disparate physical phenomena, characterized by extreme stiffness in the system of equations. The formulation -referred to as structure-preserving least-squares with variable transformation (SP-LSVT) -provides global stabilization for both implicit and explicit time integration schemes. To achieve computational efficiency, a pivoted QR decomposition is used with oversampling, and adapted to the SP-LSVT method. The framework is demonstrated in representative two-and three-dimensional reacting flow problems, and the SP-LSVT is shown to exhibit improved stability and accuracy over standard projection-based ROM techniques. Physical realizability is promoted by enforcing limiters in both temperature and species mass fractions, thus contributing to local stability enhancement. These limiters are demonstrated to be important in eliminating regions of spurious burning, thus enabling the ROMs to provide accurate representations of the heat release rate and flame propagation speed. In the 3D application, it is shown that more than two orders of magnitude acceleration in computational efficiency can be achieved, while also providing reasonable future-state predictions. A key contribution of this work is the development and demonstration of a comprehensive ROM formulation that targets highly challenging multi-scale transport-dominated problems.

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Conservative Model Order Reduction for Fluid Flow

Cited by 12 publications

References 37 publications

Investigations and Improvement of Robustness of Reduced-Order Models of Reacting Flow

Investigations and Improvement of Robustness of Reduced-Order Models of Reacting Flow

Large-eddy simulation and challenges for projection-based reduced-order modeling of a gas turbine model combustor

Model Reduction for Multi-Scale Transport Problems using Model-form Preserving Least-Squares Projections with Variable Transformation

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