Stability Properties of POD-Galerkin Approximations for the Compressible Navier-Stokes Equations

Iollo, Angelo; Lanteri, Stéphane; Désidéri, Jean‐Antoine

doi:10.1007/s001620050119

Cited by 199 publications

(133 citation statements)

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“…It is also known that for compressible flows the choice of inner product and weighting of the different flow variables (velocity, pressure, speed of sound) in the snapshot matrix can have a large effect on the stability and accuracy of the ROM [14,35]. Similarly, the H 1 inner product was recommended for the computation of POD modes for compressible Navier-Stokes equations in [66] for the purpose of enhancing stability.…”

Section: "If It Is Not In the Snapshots It Is Not In The Rom"mentioning

confidence: 99%

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

Lassila

Manzoni

Quarteroni

et al. 2014

Reduced Order Methods for Modeling and Computational Reduction

161

179

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This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities -which are mainly related either to nonlinear convection terms and/or some geometric variability -that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and -in the unsteady case -long-time stability of the reduced model. Moreover, we provide an extensive list of literature references.

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Section: "If It Is Not In the Snapshots It Is Not In The Rom"mentioning

confidence: 99%

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

Lassila

Manzoni

Quarteroni

et al. 2014

Reduced Order Methods for Modeling and Computational Reduction

161

179

View full text Add to dashboard Cite

show abstract

“…Instead of using the standard L 2 inner product in the POD, the Sobolev norm H 1 is used [38]. However, the level of dissipation has also to be fixed.…”

Section: Stabilization Of Reduced Order Modelsmentioning

confidence: 99%

Enablers for robust POD models

Bergmann

Bruneau

Iollo

2009

Journal of Computational Physics

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This paper focuses on improving the stability as well as the approximation properties of Reduced Order Models (ROM) based on Proper Orthogonal Decomposition (POD). The ROM is obtained by seeking a solution belonging to the POD subspace and that at the same time minimizes the Navier-Stokes residuals. We propose a modified ROM that directly incorporates the pressure term in the model. The ROM is then stabilized making use of a method based on the fine scale equations. An improvement of the POD solution subspace is performed thanks to an hybrid method that couples direct numerical simulations and reduced order model simulations. The methods proposed are tested on the two-dimensional confined square cylinder wake flow in laminar regime.

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“…Reduced order approximations based on the proper orthogonal decomposition (POD) and its many variants have been widely used in CFD (see, e.g., Ito et al [18], Iollo et al [17], Rowley et al [21], Bui-Thanh et al [5]), and to a limited extent in combustion dynamics (e.g., refs [14,15]). Attemts to date in combustion studies with reduced order modeling have focused on (a) developing modal analysis (POD, DMD, etc.)…”

Section: Mathematical Apparatusmentioning

confidence: 99%

“…(See, e.g., refs. [17,18] for details about this procedure). These basis functions provide a representation of the solution snapshots in the following sense.…”

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confidence: 99%

Model Reduction Opportunities in Detailed Simulations of Combustion Dynamics

Munipalli

Zhu

Menon

et al. 2014

52nd Aerospace Sciences Meeting

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Rocket and gas turbine combustion dynamics involves a confluence of diverse physics and interaction across a number of system components. Any comprehensive, self-consistent numerical model is burdened by a very large computational mesh, stiff unsteady processes which limit the permissible time step, and the need to perform tedious, repeated calculations for a broad parametric range. Predictive CFD models rely on very large scale simulations and advanced hardware. Reduced Basis Methods (RBM) have grown in usage during the past decade, as promising new techniques in making large simulations more accessible. These methods create models with far fewer unknown quantities than the original system, by generating "proper" fundamental solutions and their Galerkin projections, while guaranteeing accuracy and computational efficiency. RBMs seek to reproduce full CFD solutions, rather than solutions to a simplified or linearized set of equations. We present here some recent work in this area, focusing on approaches to model large scale combustor systems. The maturation of methods leading to LES-based turbulent combustion modeling is discussed, and model reduction goals and strategies are explored from the perspective of applicability in real life problems in both gas turbine, as well as rocket engines.

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Stability Properties of POD-Galerkin Approximations for the Compressible Navier-Stokes Equations

Cited by 199 publications

References 0 publications

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

Enablers for robust POD models

Model Reduction Opportunities in Detailed Simulations of Combustion Dynamics

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