Projection methods for reduced order models of compressible flows

Lucia, David J.; Beran, Philip S.

doi:10.1016/s0021-9991(03)00166-9

Cited by 90 publications

(48 citation statements)

References 21 publications

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“…Two techniques, Galerkin projection and direct projection, have been recently reported as having potential for obtaining nonlinear terms for POD/ROMs. 13 However, the linear portion of these realization procedures is generally unstable, requiring dissipation techniques that affect model performance. The Volterra-POD approach provides a stable reduced-order equation set, and is an important advance toward achieving stable, nonlinear reduced-order models.…”

Section: Volterra Methodsmentioning

confidence: 99%

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Aeroelastic System Development Using Proper Orthogonal Decomposition and Volterra Theory

Lucia

Beran

Silva

2005

Journal of Aircraft

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This research combines Volterra theory and proper orthogonal decomposition (POD) into a hybrid methodology for reduced-order modeling of aeroelastic systems. The outcome of the method is a set of linear ordinary differential equations (ODEs) describing the modal amplitudes associated with both the structural modes and the POD basis functions for the fluid. For this research, the structural modes are sine waves of varying frequency, and the Volterra-POD approach is applied to the fluid dynamics equations. The structural modes are treated as forcing terms which are impulsed as part of the fluid model realization. Using this approach, structural and fluid operators are coupled into a single aeroelastic operator. This coupling converts a free boundary fluid problem into an initial value problem, while preserving the parameter (or parameters) of interest for sensitivity analysis. The approach is applied to an elastic panel in supersonic cross flow. The hybrid Volterra-POD approach provides a low-order fluid model in state-space form. The linear fluid model is tightly coupled with a nonlinear panel model using an implicit integration scheme. The resulting aeroelastic model provides correct limit-cycle oscillation prediction over a wide range of panel dynamic pressure values. Time integration of the reduced-order aeroelastic model is four orders of magnitude faster than the high-order solution procedure developed for this research using traditional fluid and structural solvers.

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Section: Volterra Methodsmentioning

confidence: 99%

“…(8b). Primitive variables enable Galerkin projection for the fluid as a possible means for obtaining nonlinear terms 13 in future analysis. At Mach 1.2, LCO required about 300 time units to become fully developed, and the small, 25 time unit training window was shown to be adequate in previous work.…”

Section: Identification Of Fluid Modesmentioning

confidence: 99%

Aeroelastic System Development Using Proper Orthogonal Decomposition and Volterra Theory

Lucia

Beran

Silva

2005

Journal of Aircraft

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“…The "intrusive" approach performs a Galerkin projection of the original partial differential equations (PDEs) onto the space spanned by the reduced basis, and then it solves a system of ordinary differential equations (ODEs) for the coefficients of the linear combination [9,10]. A drawback of the Galerkin projection method is that it requires dealing with the mathematical/numerical substrate of the problem that is not always well defined or compatible with the snapshots available, such as when these snapshots are obtained from flight and/or experimental tests.…”

Section: Introductionmentioning

confidence: 99%

Local Reduced-Order Modeling and Iterative Sampling for Parametric Analyses of Aero-Icing Problems

Zhao

Habashi

Fossati³

2015

AIAA Journal

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A framework of local reduced-order modeling using machine learning algorithms is presented together with an approach to optimally select the snapshots for strongly nonlinear problems. By using an unsupervised learning algorithm, solutions are grouped into clusters of similar features. The input parameter space is divided into subregions by decision boundaries based on a supervised learning algorithm. Local reduced-order bases are extracted on each cluster, for which the solutions are represented as a linear combination of the basis vectors from their corresponding subregion. The proposed methodology is employed to conduct a comprehensive, exploration of the inflight icing certification envelopes.

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“…Two projection methods for applying this strategy in problems governed by Euler equations are presented in Ref. 4 ROMs about aeroelasticity of airfoil 5,6 and turbine engine 7 have also been derived. But all these applications above ignored the fluid viscosity.…”

Section: Introductionmentioning

confidence: 99%

Stationary flow fields prediction of variable physical domain based on proper orthogonal decomposition and kriging surrogate model

Qiu

Bai

2015

Chinese Journal of Aeronautics

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In this paper a new flow field prediction method which is independent of the governing equations, is developed to predict stationary flow fields of variable physical domain. Predicted flow fields come from linear superposition of selected basis modes generated by proper orthogonal decomposition (POD). Instead of traditional projection methods, kriging surrogate model is used to calculate the superposition coefficients through building approximate function relationships between profile geometry parameters of physical domain and these coefficients. In this context, the problem which troubles the traditional POD-projection method due to viscosity and compressibility has been avoided in the whole process. Moreover, there are no constraints for the inner product form, so two forms of simple ones are applied to improving computational efficiency and cope with variable physical domain problem. An iterative algorithm is developed to determine how many basis modes ranking front should be used in the prediction. Testing results prove the feasibility of this new method for subsonic flow field, but also prove that it is not proper for transonic flow field because of the poor predicted shock waves. ª 2015 Production and hosting by Elsevier Ltd. on behalf of CSAA & BUAA.

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Projection methods for reduced order models of compressible flows

Cited by 90 publications

References 21 publications

Aeroelastic System Development Using Proper Orthogonal Decomposition and Volterra Theory

Aeroelastic System Development Using Proper Orthogonal Decomposition and Volterra Theory

Local Reduced-Order Modeling and Iterative Sampling for Parametric Analyses of Aero-Icing Problems

Stationary flow fields prediction of variable physical domain based on proper orthogonal decomposition and kriging surrogate model

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