196,538 research outputs found
Non-Intrusive Polynomial Chaos Method Applied to Full-Order and Reduced Problems in Computational Fluid Dynamics: a Comparison and Perspectives
No full textIn this work, Uncertainty Quantification (UQ) based on non-intrusive Polynomial Chaos Expansion (PCE) is applied to the CFD problem of the flow past an airfoil with parameterized angle of attack and inflow velocity. To limit the computational cost associated with each of the simulations required by the non-intrusive UQ algorithm used, we resort to a Reduced Order Model (ROM) based on Proper Orthogonal Decomposition (POD)-Galerkin approach. A first set of results is presented to characterize the accuracy of the POD-Galerkin ROM developed approach with respect to the Full Order Model (FOM) solver (OpenFOAM). A further analysis is then presented to assess how the UQ results are affected by substituting the FOM predictions with the surrogate ROM ones
Reduced order isogeometric analysis approach for pdes in parametrized domains
No full textIn this contribution, we coupled the isogeometric analysis to a reduced order modelling technique in order to provide a computationally efficient solution in parametric domains. In details, we adopt the free-form deformation method to obtain the parametric formulation of the domain and proper orthogonal decomposition with interpolation for the computational reduction of the model. This technique provides a real-time solution for any parameter by combining several solutions, in this case computed using isogeometric analysis on different geometrical configurations of the domain, properly mapped into a reference configuration. We underline that this reduced order model requires only the full-order solutions, making this approach non-intrusive. We present in this work the results of the application of this methodology to a heat conduction problem inside a deformable collector pipe
Model Reduction Using Sparse Polynomial Interpolation for the Incompressible Navier-Stokes Equations
No full textThis work investigates the use of sparse polynomial interpolation as a model order reduction method for the parametrized incompressible Navier-Stokes equations. Numerical results are presented underscoring the validity of sparse polynomial approximations and comparing with established reduced basis techniques. Two numerical models serve to assess the accuracy of the reduced order models (ROMs), in particular parametric nonlinearities arising from curved geometries are investigated in detail. Besides the accuracy of the ROMs, other important features of the method are covered, such as offline-online splitting, run time and ease of implementation. The findings provide a clear indication that sparse polynomial interpolation is a valid instrument in the toolbox of ROM methods
A Spectral Element Reduced Basis Method in Parametric CFD
No full textWe consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14,259 degrees of freedom. The steady-state snapshot solutions define a reduced order space, which allows to accurately evaluate the steady-state solutions for varying Reynolds number with a reduced order model within a fixed-point iteration. In particular, we compare different aspects of implementing the reduced order model with respect to the use of a spectral element discretization. It is shown, how a multilevel static condensation (Karniadakis and Sherwin, Spectral/hp element methods for computational fluid dynamics, 2nd edn. Oxford University Press, Oxford, 2005) in the pressure and velocity boundary degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios
Basic ideas and tools for projection-based model reduction of parametric partial differential equations
No full textWe provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions, offline-online decomposition and error estimation is introduced. Several tools for geometry parametrizations, such as free form deformation, radial basis function interpolation and inverse distance weighting interpolation are explained. The empirical interpolation method is introduced as a general tool to deal with non-affine parameter dependency and non-linear problems. The discrete and matrix versions of the empirical interpolation are considered as well. Active subspaces properties are discussed to reduce high-dimensional parameter spaces as a pre-processing step. Several examples illustrate the methodologies
POD-Galerkin model order reduction for parametrized nonlinear time-dependent optimal flow control: An application to shallow water equations
No full textIn the present paper we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal with is nonlinear and time dependent: this leads to very time consuming simulations which can be unbearable, e.g., in a marine environmental monitoring plan application. Our aim is to show how reduced order modelling could help in studying different configurations and phenomena in a fast way. After building the optimality system, we rely on a POD-Galerkin reduction in order to solve the optimal control problem in a low dimensional reduced space. The presented theoretical framework is actually suited to general nonlinear time dependent optimal control problems. The proposed methodology is finally tested with a numerical experiment: the reduced optimal control problem governed by shallow waters equations reproduces the desired velocity and height profiles faster than the standard model, still remaining accurate
Rec. a Iacopo Sannazaro tra latino e volgare, Atti del Convegno di Studi in ricordo di Marco Santagata (Pisa, 8-9 luglio 2021), cur. M. Landi, M. Riccucci, Pisa, Pisa University Press, 2023, pp. 315, ISBN 978- 88-3339-763-4.
No full textCombined parameter and model reduction of cardiovascular problems by means of active subspaces and POD-Galerkin methods
No full textIn this chapter we introduce a combined parameter and model reduction
methodology and present its application to the efficient numerical estimation
of a pressure drop in a set of deformed carotids. The aim is to simulate a wide
range of possible occlusions after the bifurcation of the carotid. A parametric
description of the admissible deformations, based on radial basis functions
interpolation, is introduced. Since the parameter space may be very large, the
first step in the combined reduction technique is to look for active subspaces
in order to reduce the parameter space dimension. Then, we rely on model order
reduction methods over the lower dimensional parameter subspace, based on a
POD-Galerkin approach, to further reduce the required computational effort and
enhance computational efficiency
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