Hi-POD Solution of Parametrized Fluid Dynamics Problems: Preliminary Results

Baroli, Davide; Cova, Cristina Maria; Perotto, Simona; Sala, Lorenzo; Veneziani, Alessandro

doi:10.1007/978-3-319-58786-8_15

Cited by 17 publications

(29 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A possible future development of this work might concern the integration of the proposed methods into a FSI solver or the application to several optimization contexts. An adaptive selection of the control points driven by some quantity of interest, combination with reduction procedures for parametrized problems (eg, the works of Hesthaven et al, Baroli et al, and Chinesta et al), as well as the use of active subspaces method as preprocessing, represent further topics of interest for the following of the current work.…”

Section: Discussionmentioning

confidence: 99%

A POD‐selective inverse distance weighting method for fast parametrized shape morphing

Ballarin

D'Amario

Perotto

et al. 2018

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

Summary Efficient shape morphing techniques play a crucial role in the approximation of partial differential equations defined in parametrized domains, such as for fluid‐structure interaction or shape optimization problems. In this paper, we focus on inverse distance weighting (IDW) interpolation techniques, where a reference domain is morphed into a deformed one via the displacement of a set of control points. We aim at reducing the computational burden characterizing a standard IDW approach without significantly compromising the accuracy. To this aim, first we propose an improvement of IDW based on a geometric criterion that automatically selects a subset of the original set of control points. Then, we combine this new approach with a dimensionality reduction technique based on a proper orthogonal decomposition of the set of admissible displacements. This choice further reduces computational costs. We verify the performances of the new IDW techniques on several tests by investigating the trade‐off reached in terms of accuracy and efficiency.

show abstract

Section: Discussionmentioning

confidence: 99%

A POD‐selective inverse distance weighting method for fast parametrized shape morphing

Ballarin

D'Amario

Perotto

et al. 2018

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…This apparent drawback has a negligible impact from an operative standpoint because the computational time required to compute the POD basis is much smaller than the time required for a full simulation step. As a future development, it would be interesting to extend the range of applicability of our approach by using more sophisticated model reduction methods, e.g., by coupling our strategy with Lagrangian based model reduction [33] or by resorting to more recent techniques such as hierarchical model reduction [2,37]. 3.…”

Section: Discussionmentioning

confidence: 99%

Adaptive POD model reduction for solute transport in heterogeneous porous media

et al. 2017

Self Cite

View full text Add to dashboard Cite

We study the applicability of a model order reduction technique to the solution of transport of passive scalars in homogeneous and heterogeneous porous media. Transport dynamics are modeled through the advection-dispersion equation (ADE) and we employ Proper Orthogonal Decomposition (POD) as a strategy to reduce the computational burden associated with the numerical solution of the ADE. Our application of POD relies on solving the governing ADE for selected times, termed snapshots. The latter are then employed to achieve the desired model order reduction. We introduce a new technique, termed Snapshot Splitting Technique (SST), which allows enriching the dimension of the POD subspace and damping the temporal increase of the modeling error. Coupling SST with a modeling strategy based on alternating over diverse time scales the solution of the full numerical transport model to its reduced counterpart allows extending the benefit of POD over a prolonged temporal window so that the salient features of the process can be captured at a reduced computational cost. The selection of the time scales across which the solution of the full and reduced model are alternated is linked to the Péclet number (P e), representing the interplay between advective and dispersive processes taking place in the system. Thus, the method is adaptive in space and time across the heterogenous structure of the domain through the combined use of POD and SST and by way of alternating the solution of the full and reduced models. We find that the width of the time scale within which the PODbased reduced model solution provides accurate results tends to increase with decreasing P e. This suggests that the effects of local scale dispersive processes facilitate the POD method to capture the salient features of the system dynamics embedded in the selected snapshots. Since the dimension of the reduced model is much lower than that of the full numerical model, the methodology we propose enables one to accurately simulate transport at a markedly reduced computational cost.

show abstract

“…The parametric counterpart of the HiMod reduction, known as HiPOD, merges HiMod with POD [4,13]. HiPOD pursues a different goal with respect to PGD.…”

Section: Himod Reduction and Pgd For Parametrized Problemsmentioning

confidence: 99%

“…The parametric version of HiMod (namely, HiPOD) is a more recent proposal [4,13]. On the other hand, PGD is not so widely employed in a non-parametric setting, despite its original formulation [12].…”

Section: Introductionmentioning

confidence: 99%

Model Reduction by Separation of Variables: A Comparison Between Hierarchical Model Reduction and Proper Generalized Decomposition

Perotto

Carlino

Ballarin

2020

Lecture Notes in Computational Science and Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

Hi-POD Solution of Parametrized Fluid Dynamics Problems: Preliminary Results

Abstract: Numerical modeling of fluids in pipes or network of pipes (like in the circulatory system) has been recently faced with new methods that exploit the specific nature of the dynamics, so that a one dimensional axial mainstream is enriched by local secondary transverse components (

Cited by 17 publications

References 23 publications

A POD‐selective inverse distance weighting method for fast parametrized shape morphing

A POD‐selective inverse distance weighting method for fast parametrized shape morphing

Adaptive POD model reduction for solute transport in heterogeneous porous media

Model Reduction by Separation of Variables: A Comparison Between Hierarchical Model Reduction and Proper Generalized Decomposition

Contact Info

Product

Resources

About