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See detailA hyper-reduction method using adaptivity to cut the assembly costs of reduced order models
Hale, Jack UL; Schenone, Elisa; Baroli, Davide UL et al

E-print/Working paper (2019)

At every iteration or timestep of the online phase of some reduced-order modelling schemes, large linear systems must be assembled and then projected onto a reduced order basis of small dimension. The ... [more ▼]

At every iteration or timestep of the online phase of some reduced-order modelling schemes, large linear systems must be assembled and then projected onto a reduced order basis of small dimension. The projected small linear systems are cheap to solve, but assembly and projection are now the dominant computational cost. In this paper we introduce a new hyper-reduction strategy called reduced assembly (RA) that drastically cuts these costs. RA consists of a triangulation adaptation algorithm that uses a local error indicator to con- struct a reduced assembly triangulation specially suited to the reduced order basis. Crucially, this reduced assembly triangulation has fewer cells than the original one, resulting in lower assembly and projection costs. We demonstrate the efficacy of RA on a Galerkin-POD type reduced order model (RAPOD). We show performance increases of up to five times over the baseline Galerkin-POD method on a non-linear reaction-diffusion problem solved with a semi-implicit time-stepping scheme and up to seven times for a 3D hyperelasticity problem solved with a continuation Newton-Raphson algorithm. The examples are implemented in the DOLFIN finite element solver using PETSc and SLEPc for linear algebra. Full code and data files to produce the results in this paper are provided as supplementary material. [less ▲]

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See detailModelling and analysis of flow-driven energy harvesting devices and associated reduced order models
Zilian, Andreas UL; Baroli, Davide UL

Scientific Conference (2018, June)

A specific class of energy harvester devices for renewable energy resources allows conversion of ambient fluid flow energy to electrical energy via flow-induced vibrations of a piezo-ceramic composite ... [more ▼]

A specific class of energy harvester devices for renewable energy resources allows conversion of ambient fluid flow energy to electrical energy via flow-induced vibrations of a piezo-ceramic composite structure positioned in the flow field. This energy converter technology simultaneously involves the interaction of a composite structure and a surrounding fluid, the electric charge accumulated in the piezo-ceramic material and a controlling electrical circuit. In order to predict the efficiency and operational properties of such future devices and to increase their robustness and performance, a mathematical and numerical model of the complex physical system is required to allow systematic computational investigation of the involved phenomena and coupling characteristics. The presentation will discuss a monolithic modelling approach that allows simultaneous analysis of the harvester, which involves surface-coupled fluid-structure interaction, volume-coupled electro-mechanics and a controlling energy harvesting circuit. Based on a finite element discretisation of the weighted residual form of the governing equations, time- and frequency-domain analysis enables investigation of different types of structures (plate, shells) subject to exterior/interior flow with varying parameters, and attached electrical circuits with respect to the electrical power output generated. Consequently, options for parametric reduced-order modelling of flow-driven energy harvesters will be discussed. [less ▲]

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See detailComparison of Several RANS Modelling for the Pavia TRIGA Mark II Research Reactor
Introini, Carolina; Cammi, Antonio; Lorenzi, Stefano et al

in Journal of Nuclear Engineering and Radiation Science (2018)

Aim of this work is the comparison of different turbulent models based on the Reynolds Averaged Navier-Stokes (RANS) equations in order to find out which model is the most suitable for the study of the ... [more ▼]

Aim of this work is the comparison of different turbulent models based on the Reynolds Averaged Navier-Stokes (RANS) equations in order to find out which model is the most suitable for the study of the channel thermal-hydraulics of the TRIGA Mark II reactor. Only the steady state behaviour (i.e. the full power stationary operational conditions) of the reactor has been considered. To this end, the RAS (Reynolds-Averaged Simulation) models available in the open source CFD software OpenFOAM have been applied to the most internal channel of the TRIGA and assessed against a Large Eddy Simulation (LES) model. The results of the latter approach, expressed in terms of axial velocity, turbulent viscosity, turbulent kinetic energy, and temperature have been compared with the results obtained by the RAS models available in OpenFOAM (k − ε, k − ω and Reynolds Stress Transport). Heat transfer is taken into account as well by means of the turbulent energy diffusivity parameter. The simulation results demonstrate how, amongst the RAS models, the k − ω SST is the one whose results are closer to the LES simulation. This model seems to be the best one for the treatment of turbulent flow within the TRIGA subchannel, offering a good compromise between accuracy and computational requirements. Since it is much less expensive than an LES model, it can be applied even to full core calculation, in order to obtain accurate results with less computational effort. [less ▲]

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See detailHi-POD solution of parametrized fluid dynamics problems: preliminary results
Baroli, Davide UL; Cova, Maria Cristina; Perotto, Simona et al

in MS&A series (2018), MS&A series(3),

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 ... [more ▼]

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 [4, 16, 18]. These methods - under the name of Hi-Mod approximation - construct a solution as a finite element axial discretization, completed by a spectral approximation of the transverse dynamics. It has been demonstrated that Hi-Mod reduction significantly accelerates the computations without com- promising the accuracy. In view of variational data assimilation procedures (or, more in general, control problems), it is crucial to have efficient model reduction techniques to rapidly solve, for instance, a parametrized problem for several choices of the parameters of interest. In this work, we present some preliminary results merging Hi-Mod techniques with a classical Proper Orthogonal Decomposition (POD) strategy. We name this new approach as Hi-POD model reduction. We demonstrate the efficiency and the reliability of Hi-POD on multiparameter advection-diffusion-reaction problems as well as on the incompressible Navier-Stokes equations, both in a steady and in an unsteady setting. [less ▲]

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See detailA Reduced Order Kalman Filter for Computational Fluid-Dynamics Applications
Introini, Carolina; Cammi, Antonio; Lorenzi, Stefano et al

Poster (2018)

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See detailDevelopment of a Data-Driven Approach based on Kalman filtering for CFD Reactor Analysis
Introini, Carolina; Cammi, Antonio; Lorenzi, Stefano et al

in PHYSOR 2018 (2018)

In the last several years, computer-based simulation has become an important analysis and design tool in many engineering fields. The common practice involves the use of low-fidelity models, which in most ... [more ▼]

In the last several years, computer-based simulation has become an important analysis and design tool in many engineering fields. The common practice involves the use of low-fidelity models, which in most cases are able to provide fairly accurate results while maintaining a low computational cost. However, for complex systems such as nuclear reactors, more detailed models are required for the in-depth analysis of the problem at hand, due for example to the complex geometries of the physical domain. Nevertheless, such models are affected by potentially critical uncertainties and inaccuracies. In this context, the use of data assimilation methods such as the Kalman filter to integrate local experimental data witihin the numerical model looks very promising as a high-fidelity analysis tool. In this work, the focus is the application of such methods to the problem of fluid-dynamics analysis of the reactor. Indeed, in terms of nuclear reactor investigation, a detailed characterization of the coolant behaviour within the reactor core is of manda- tory importance in order to understand, among others, the operating conditions of the system, and the potential occurrence of accident scenarios. In this context, the use of data assimilation methods allows the extraction of information of the thermo-dynamics state of the system in a benchmarked transitory in order to increase the fidelity of the com- putational model. Conversely to the current application of control-oriented black-box in the nuclear energy community, in this work the integration of the data-driven paradigm into the numerical formulation of the CFD problem is proposed. In particular, the al- gorithm outlined embeds the Kalman filter into a segregated predictor-corrector formu- lation, commonly adopted for CFD analysis. Due to the construction of the developed method, one of the main challenges achieved is the preservation of mass-conservation for the thermo-dynamics state during each time instant. As a preliminary verification, the proposed methodology is validated on a benchmark of the lid-driven cavity. The obtained results highlight the efficiency of the proposed method with respect to the state-of-art low fidelity approach. [less ▲]

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See detailReduced basis Nitsche-based domain decomposition: a biomedical application
Baroli, Davide UL; Beex, Lars UL; Hale, Jack UL et al

Scientific Conference (2017, March 10)

Nowadays, the personalized biomedical simulations demand real-time efficient and reliable method to alleviate the computational complexity of high-fidelity simulation. In such applications, the necessity ... [more ▼]

Nowadays, the personalized biomedical simulations demand real-time efficient and reliable method to alleviate the computational complexity of high-fidelity simulation. In such applications, the necessity of solving different substructure, e.g. tissues or organs, with different numbers of the degrees of freedom and of coupling the reduced order spaces for each substructure poses a challenge in the on-fly simulation. In this talk, this challenge is taken into account employing the Nitsche-based domain decomposition technique inside the reduced order model [1]. This technique with respect to other domain decomposition approach allows obtaining a solution with the same accuracy of underlying finite element formulation and to flexibly treat interface with non-matching mesh. The robustness of the coupling is determined by the penalty coefficients that is chosen using ghost penalty technique [2]. Furthermore, to reduce the computational complexity of the on-fly assembling it is employed the empirical interpolation approach proposed in [3]. The numerical tests, performed using FEniCS[4], petsc4py and slepc4py [5], shows the good performance of the method and the reduction of computation cost. [1] Baroli, D., Beex L. and Bordas, S. Reduced basis Nitsche-based domain decomposition. In preparation. [2] Burman, E., Claus, S., Hansbo, P., Larson, M. G., & Massing, A. (2015). CutFEM: Discretizing geometry and partial differential equations. International Journal for Numerical Methods in Engineering, 104(7), 472-501. [3] E. Schenone, E., Beex,L., Hale, J.S., Bordas S. Proper Orthogonal Decomposition with reduced integration method. Application to nonlinear problems. In preparation. [4] A. Logg, K.-A. Mardal, G. N. Wells et al. Automated Solution of Differential Equations by the Finite Element Method, Springer 2012. [5] L. Dalcin, P. Kler, R. Paz, and A. Cosimo, Parallel Distributed Computing using Python, Advances in Water Resources, 34(9):1124-1139, 2011. http://dx.doi.org/10.1016/j.advwatres.2011.04.013 [less ▲]

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See detailComparison of Several RANS Modelling for the Pavia TRIGA Mark II Research Reactor
Introini, Carolina; Baroli, Davide UL; Peters, Bernhard UL

Poster (2017)

In this study, a detailed analysis of the turbulent regime within the core of the Pavia TRIGA Mark II reactor is perfomed by means of an in-depth comparison of the RAS (Reynolds-Averaged Simulation ... [more ▼]

In this study, a detailed analysis of the turbulent regime within the core of the Pavia TRIGA Mark II reactor is perfomed by means of an in-depth comparison of the RAS (Reynolds-Averaged Simulation) turbulence models implemented in OpenFOAM. Aim of this analysis is to give some important information with respect to the flow regime within the core. The performance of the various models is tested against a LES (Large Eddy Simulation) of the innermost channel. [less ▲]

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See detailImage to analysis pipeline: single and double balloons kyphoplasty
Baroli, Davide UL; Hauseux, Paul UL; Hale, Jack UL et al

Poster (2016, December 12)

In this work, we present a semi-automatic pipeline from image to simulation of a patient fractured vertebra after the kyphoplastic augmentation with two balloons. In this procedure, the CT-scan medical ... [more ▼]

In this work, we present a semi-automatic pipeline from image to simulation of a patient fractured vertebra after the kyphoplastic augmentation with two balloons. In this procedure, the CT-scan medical image are pre-processed using open-source software Slice3D for segmentation and 3D reconstruction operation. Then, using geometric processing the 3D surface geometry is enhanced to avoid degenerate element and trigging phenomena on vertebra and cement area. We perform a finite element analysis to evaluate the risk of subsequent vertebral fracture. Finally using Monte-Carlo technique, we assess the propagation of uncertainty of material parameter on the evaluation of this risk. Based on the developed semi-automatic pipelines, it is possible to perform a patient-specific simulation that assesses the successful of kyphoplasty operation. [less ▲]

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See detailReduced order method combined with domain decomposition
Baroli, Davide UL; Bordas, Stéphane UL; Beex, Lars UL et al

Scientific Conference (2016)

The complexities and nonlinearity of the PDEs in biomechanics and the requirement for rapid solution pose significant challenges for the biomedical applications. For these reasons, different methods for ... [more ▼]

The complexities and nonlinearity of the PDEs in biomechanics and the requirement for rapid solution pose significant challenges for the biomedical applications. For these reasons, different methods for reducing the complexity and solving efficiently have been investigated in the last 15 years. At the state-ofart, due to spatial different behaviours and highly accurate simulation required, a decomposition of physical domain is deeply investigated in reduced basis element method approaches. In this talk, the main focus is devoted to present suitable reduction strategy which combines a domain decomposition approach and a proper interface management with a proper orthogonal decomposition. We provide numerical tests implemented in DOLFIN[4] using SLEPc [3] and PETSc [1, 2] that show a speed up in forward runtime model. [less ▲]

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See detailA mass conservative Kalman filter algorithm for thermo-computational fluid dynamics
Introini, Carolina; Baroli, Davide UL; Lorenzi, Stefano et al

in Materials (ISSN 1996-1944) (n.d.)

Computational fluid-dynamics (CFD) is of wide relevance in engineering and science, due to its capability of simulating the three-dimensional flow at various scales. However, the suitability of a given ... [more ▼]

Computational fluid-dynamics (CFD) is of wide relevance in engineering and science, due to its capability of simulating the three-dimensional flow at various scales. However, the suitability of a given model depends on the actual scenarios which are encountered in practice. This challenge of model suitability and calibration could be overcome by a dynamic integration of measured data into the simulation. This paradigm is known as data-driven assimilation (DDA). In this paper, the study is devoted to Kalman filtering, a Bayesian approach, applied to Reynolds-Averaged Navier-Stokes (RANS) equations for turbulent flow. The integration of the Kalman estimator into the PISO segregated scheme was recently investigated by (1). In this work, this approach is extended to the PIMPLE segregated method and to the ther- modynamic analysis of turbulent flow, with the addition of a sub-stepping procedure that ensures mass conservation at each time step and the com- patibility among the unknowns involved. The accuracy of the algorithm is verified with respect to the heated lid-driven cavity benchmark, incorporat- ing also temperature observations, comparing the augmented prediction of the Kalman filter with the CFD solution obtained on a very fine grid. [less ▲]

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See detailCoupled Molecular Dynamics and Finite Element Method: simulations of kinetics induced by field mediated interaction
Cascio, Michele; Baroli, Davide UL; Deretzsis, Ioannis et al

in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (n.d.)

A computational approach coupling Molecular Dynamics (MD)-Finite Element Method (FEM) techniques is here proposed for the theoretical study of the dynamics of particles subjected to the electromechanical ... [more ▼]

A computational approach coupling Molecular Dynamics (MD)-Finite Element Method (FEM) techniques is here proposed for the theoretical study of the dynamics of particles subjected to the electromechanical forces. The system consists in spherical particles (modeled as micrometric rigid bodies with proper densities and dielectric functions) suspended in a colloidal solution which flows in a microfluidic channel in the presence of a generic non-uniform variable electric field, generated by electrodes. The particles are subjected to external forces (e.g. drag or gravity) which satisfy the particle-like formulation, typical of the MD approach, and to electromechanical force which in turn needs, during the equation of the motion integration, the self-consistent solutions in three dimensions of correct continuum field equation. In the MD-FEM method used in this work, Finite Element Method is applied to solve the continuum field equation and MD technique is applied to the stepwise explicit integration of equation of the motion. Our work shows the potential of coupled MD-FEM for the study of electromechanical particles and opens the double perspective to use a) MD away from the field of the atomistic simulation and b) the continuum/particle approach to another case where the conventional forces’ evaluation method used in MD is not applicable. [less ▲]

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