# Summer School on Reduced Order Methods in Computational Fluid Dynamics

Europe/Rome
SISSA, International School for Advanced Studies, Main Campus, Trieste, Italy

#### SISSA, International School for Advanced Studies, Main Campus, Trieste, Italy

Via Bonomea 265, 34136 Trieste, Italy
Description

## The scope and the structure of the Summer School

The scope of the summer school is to provide an overview of reduced order methods with particular emphasis on fluid dynamics problem. The school will start with a brief introduction on the different full order discretization techniques usually employed in computational fluid dynamics (Finite Element and Finite Volume Method) and will later introduce different reduced order modeling strategies. The methodologies introduced during the classes will also be employed during practical exercises using the computational framework developed at SISSA (RBniCS/ITHACA-FV).

SISSA Lecturers: Gianluigi Rozza, Francesco BallarinGiovanni Stabile.

Guest Lecturers: Annalisa Quaini (University of Houston), Simona Perotto (Politecnico di Milano) , Matteo Giacomini (Polytechnic University of Catalonia).

Thematic lectures offered by SISSA staff: Enrique DelgadoNicola Demo, Michele GirfoglioMartin Hess, Efthymios Karatzas, Andrea Lario, Andrea MolaFederico Pichi, Maria Strazzullo, Marco Tezzele, Zakia Zainib

Scientific Committee: Gianluigi Rozza, Francesco BallarinGiovanni Stabile.

Organizing Committee: Francesco Ballarin, Giuseppe Carere, Enrique Delgado, Nicola Demo, Michele Girfoglio, Sara Greblo, Martin Hess, Saddam Hijazi, Efthymios Karatzas, Andrea Lario, Laura Meneghetti, Andrea Mola, Umberto Morelli, Monica Nonino, Federico Pichi, Francesco Romor, Gianluigi Rozza, Nirav Shah, Giovanni Stabile, Maria Strazzullo, Marco Tezzele, Emanuele Tuillier Illingworth, Zakia Zainib, Matteo Zancanaro (SISSA), Shafqat Ali (ICTP).

The Summer School will be of 5 days; Also, there will be a poster session open to students and early postdocsParticipants are encouraged to prepare a poster that summarizes their research activity that will be presented during the summer school.

The Summer School is among the flagship events sponsored by the European Mathematical Society.

The event is also among the proESOF initiatives.

The school is organized in cooperation with SISSA SIAM student chapter

Contact
• Monday, 8 July
• 10:30 12:45
Software Installation Support (confirmed with appointment) 2h 15m
• 13:45 14:00
Opening 15m
• 14:00 14:45
Introduction on Reduced Order Methods in CFD: State of the art and Perspectives 45m
Speaker: Prof. Gianluigi Rozza
• 14:45 15:30
A brief Technical Introduction on Reduced Order Methods based on Galerkin Projection 45m
Speaker: Prof. Gianluigi Rozza
• 15:30 16:00
Coffe Break 30m
• 16:00 16:45
Basics Of the Finite Element Method 45m
Speaker: Dr Francesco Ballarin
• 16:45 18:00
Reduced Basis for Finite Element Problems 1h 15m
Speaker: Dr Francesco Ballarin
• Tuesday, 9 July
• 09:00 09:45
A posteriori error estimation for certified reduced basis methods 45m
Speaker: Dr Francesco Ballarin (SISSA)
• 09:45 10:30
Non-affine (and nonlinear) problems 45m
Speaker: Dr Francesco Ballarin (SISSA)
• 10:30 11:00
Coffe Break 30m
• 11:00 11:45
Installation of the software packages - Session 2 45m
• 11:45 12:30
Practical Session with RBniCS I : worked problems 45m
Speaker: Dr Francesco Ballarin et al. (SISSA)
• 12:30 14:00
Lunch Break 1h 30m
• 14:00 14:45
Practical Session with RBniCS II : worked problems 45m
Speaker: Dr Francesco Ballarin et al. (SISSA)
• 14:45 15:30
Certified Smagorinsky reduced basis turbulence model 45m
• 15:30 16:00
Coffe Break 30m
• 16:00 17:00
Reduced Order Methods for Flow Control 1h
Speakers: Maria Strazzullo (SISSA, mathlab), Zakia Zainib (SISSA mathLab)
• 17:00 17:30
Parametric reduced order methods for computational hemodynamics simulations 30m
Speakers: Francesco Ballarin (SISSA mathLab), Zakia Zainib (mathlab, Mathematics area, SISSA)
• 17:30 18:15
Reduced order modelling in bifurcating parametrised non-linear equations 45m
Speaker: Federico Pichi (Scuola Internazionale Superiore di Studi Avanzati - SISSA)
• Wednesday, 10 July
• 09:00 10:30
Introduction on the Finite Volume Method and turbulence modelling 1h 30m
Speakers: Dr Giovanni Stabile, Dr Michele Girfoglio
• 10:30 11:00
Coffe Break 30m
• 11:00 12:30
Computational reduction for CFD problems with turbulence 1h 30m
Speaker: Dr Giovanni Stabile
• 12:30 14:00
Lunch Break 1h 30m
• 14:00 14:45
Best Practices in Programming 45m
Speaker: Nicola Demo (MHPC)
• 14:45 15:30
Weighted Reduced Order approaches for Uncertainty Quantification 45m
Speaker: Prof. Gianluigi Rozza (Full professor)
• 15:30 16:00
Coffe Break 30m
• 16:00 17:30
Poster blitz
• 16:00
Non-intrusive reduced order models for the shallow water equations 3m

Proper Orthogonal Decomposition (POD)-based model order reduction techniques are a popular choice for multi-query and fast replay applications in CFD, which often require sophisticated extensions for efficient treatment of nonlinearities. Non-intrusive methods which treat the high fidelity model as an external black-box offer a desirable alternative.
We present a non-intrusive approach which replaces the projected reduced model with a multidimensional radial basis function (RBF) interpolant. We evaluate several greedy strategies for the selection of optimal quadrature points that can effectively capture the temporal dynamics.

We compare the performance of classical kernel-based non-intrusive techniques and temporally optimized quadrature points for shallow water flow applications across a range of fluid regimes like riverine flows, flow in estuaries as well as large-scale geophysical flows. The accuracy, computational expense, and robustness of the RBF non-intrusive method are also evaluated in comparison to a traditional nonlinear POD strategy.

Speaker: Dr Sourav Dutta (US Army Engineer Research and Development Center)
• 16:03
Reduction of the Kolmogorov $n$-width for a transport dominated fluid-structure interaction problem 3m

The aim of the work is to apply the reduced basis method to a two dimensional time dependent convection dominated fluid-structure interaction (FSI) problem.
One basic assumption of the reduced basis method is that the solution manifold $\mathcal{M}$ of the problem
can be well approximated by a sequence of finite dimensional spaces: this mathematical assumption translates in the fact that the Kolmogorov n-width $D_n$ of $\mathcal{M}$ decays fast.
For convection dominated problems this is not always the case, meaning that $D_n$ can decay quite slowly, and this represents a great challenge for the reduced method.
We will show how we tried to overcome this situation, explaining the idea presented in [3]: the main feature of this new reduced method is the presence of a preprocessing phase, which is performed right after the offline step. Assume that $\Omega$ is the physical domain of the problem of interest: the preprocessing phase is based on the definition of a family $\mathcal{F}$ of smooth and invertible deformation maps of $\Omega$, such that the preprocessed'' solution manifold $\mathcal{M}_{\mathcal{F}}$ has a smaller Kolmogorov $n$-width, where $\mathcal{M}_{\mathcal{F}}$ is the manifold of the solutions on the deformed domain. We will explain how to construct this family of mappings, once we have shown the behaviour of the solution of the specific problem.
After the POD on the preprocessed solution manifold we obtain a set of preprocessed reduced bases $\{\Phi_i\}_{i=1}^N$, with $N$ small. With these preprocessed basis functions we then try to construct an approximation of the high order solution.
In our poster we will show the results we obtained so far, and we will also discuss some of the difficulties we encountered during this work: the attention that is required in handling the coupling conditions between
the fluid equations and the structure equation, the search for a suitable family of deformation maps, and also the very important aspect of how to interpret the rate of decay of the Kolmogorov $n$-width of the original solution manifold for this particular problem.

[1] Ballarin F. and Rozza G., POD-Galerking monolithic reduced order models for parametrized fluid-structure interaction problems. IJNMF: 82(12):1010--1034, 2016.
[2] Ballarin F., Rozza G. and Maday Y., Reduced-order semi-implicit schemes for fluid-structure interaction problems. MSA vol.17: 149-167, Springer International Publishing, 2017.
[3] Cagniart N., Maday Y. and Stamm B., Model order reduction for problems with large convection effects, 2016.

Speaker: Ms Monica Nonino (SISSA)
• 16:06
Multi-scale numerical modeling of sorption kinetics 3m

The trapping of diffusing particles by either a single or a distribution of moving traps is an interesting topic that has been employed to model a variety of different real problems in chemistry, physics and biology. Here we study the dynamics of diffusing particles in a domain with an oscillating bubble. Laboratory experiments provide evidence of a non monotone behavior in time of the concentration of particles by a detector located behind the bubble, under suitable experimental condition. A comprehensive explanation of the phenomenon is not yet fully available.
The particles are attracted and trapped near the surface of the bubble. The basic mathematical model is a drift-diffusion model, where the particles diffuse and feel the potential of the bubble when they are near its surface. The numerical simulation of the system presents two multi-scale challenges. One is spatial: the range of the bubble potential is confined within a few microns at the bubble surface, while the bubble radius is of the order of a millimeter, so a fully resolved solution would be too expensive. The second challenge is on the time scale: the bubble oscillates with a frequency of the order of 100 Hz, while the diffusion time scale is of the order of 103 seconds, this requiring at least 106 time steps to fully resolve the problem in time.
A reduced model is derived to solve the multi-scale problem it space: the interaction with the bubble is modeled as a very thin layer, with a particle surface density proportional to the local density in the bulk, near the bubble. In the rest of the domain the particle density satisfies just a diffusion equation, with suitable boundary conditions on the bubble, deduced from conservation properties.
The model is carefully tested on problems in 1D, 2D planar and 3D axis-symmetric geometry. The equation is discretized on a regular Cartesian mesh, using a ghost-point approach, and solved by Crank-Nicolson scheme. The implicit step is efficiently solved by a suitably adapted multi-grid method.
The amplitude of the bubble oscillations is small compared to the bubble radius. We take advantage of this fact by replacing the time dependent position by imposing a suitable time dependent velocity at the bubble surface. Because of the low Reynolds number, the velocity distribution is computed by Stokes approximation.
The multi-scale challenge in time is still under investigation.

Speaker: Dr Clarissa Astuto (University of Catania)
• 16:09
Reduced basis methods for parametric bifurcation problems in nonlinear PDEs 3m

The aim of this work is to show the applicability of the reduced basis model reduction in non-linear systems undergoing bifurcations. Bifurcation analysis, i.e., following the different bifurcating branches, as well as determining the bifurcation points themselves, is a complex computational task [1, 4]. Reduced Order Models (ROM) can potentially reduce the computational burden by several orders of magnitude.
Models describing bifurcating phenomena arising in several fields with interesting applications, from continuum to quantum mechanics passing through fluid dynamics.
We first focus on non-linear structural mechanics [3], and we show applications of ROM to Von Kármán plate equations and to an hyperelastic 3D beam.
Then we consider the incompressible Navier-Stokes equations in a channel [1] discretized with the spectral element method, which undergoes bifurcations with increasing Reynolds.
Finally, we show some recent results of the bifurcating phenomena in Bose-Einstein condensates (BEC) varying the chemical parameter [2].
Some of these studies are carried out in collaboration with A.T. Patera at MIT, A. Quaini at University of Houston and F. Ballarin, M. Hess at SISSA.

References

[1] A. Alla, M. Gunzburger, M. W. Hess, A. Quaini, and G. Rozza. A localized reduced-order modeling approach for pdes with bifurcating solutions. Computer Methods in Applied Mechanics and Engineering, 351:379 – 403, 2019.
[2] F. Pichi, A. Quaini, and G. Rozza. Reduced technique in bifurcating phenomena: application to the Gross-Pitaevskii equation. In preparation, 2019.
[3] F. Pichi and G. Rozza. Reduced basis approaches for parametrized bifurcation problems held by nonlinear Von Kármán equations. Submitted, https://arxiv.org/abs/1804.02014, 2018.
[4] G. Pitton, A. Quaini, and G. Rozza. Computational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: applications to coanda effect in cardiology. Journal of Computational Physics, 344:534–557, 2017.

Speaker: Mr Federico Pichi (Scuola Internazionale Superiore di Studi Avanzati - SISSA)
• 16:12
Model-Order Reduction for 3D Turbulent Mixing T-junction 3m

We consider a model-order reduction approach to approximate scalar transport
and mixing in a T-junction using spectral-element-based large-eddy simulation
(LES) for the full-order model. One such LES simulation of 100 convective-time
units can cost hundreds of thousands of core-hours on a supercomputer. For the
reduced-order model, we apply Galerkin projection using POD-generated global
basis functions to reproduce the quantity of interest, the concentration
profile of the passive scalar. For turbulent flows, the Galerkin formulation
applied to a small number of dominant POD modes may not be sufficient to remain
in the basin of attraction of the underlying dynamics. The reason that is
typically cited for this behavior is the inability of this combination to
sufficiently dissipate energy since the POD modes lack the small-scale
structures found in such flows. By introducing a stabilization mechanism,
significant improvement in accuracy can be achieved. Here, we describe recent
results using POD-Galerkin projection with constrained optimization to ensure
that the flow evolves within the dynamical range observed in the full-order
model. With this approach, we address the turbulent flow reproduction problem,
which is a first step towards parametric model order reduction for turbulent
thermal transport.

Speakers: Mr Kento Kaneko (University of Illinois at Urbana-Champaign), Mr Ping-Hsuan Tsai (UIUC)
• 16:15
Finite volume POD-Galerkin Reduced Order Model of the Boussinesq approximation for buoyancy-driven flow 3m

To model the complex dynamics of buoyancy for nuclear thermal-hydraulic studies and other similar industrial problems, a two-way coupling between the momentum equations and the energy equation is required. To simplify the problem, the Boussinesq approximation is often applied by neglecting the effect of local density differences of the fluid, induced by temperature, except for the density variation in the gravitational body force term.
However, to model buoyancy-driven flows using a full numerical approach is completely unfeasibly for many applications due to the excessive amount of computational time and power needed, especially when a large number of different system configurations are to be tested for control purposes, sensitivity analyses or uncertainty quantification studies.
Therefore, a parametric Reduced Order Model (ROM) of the Boussinesq approximation is developed for which the Full Order Model (FOM) is based on the finite volume approximation. A Proper Orthogonal Decomposition (POD) approach is used for the construction of a reduced basis on which a Galerkin projection of the governing equations is performed to obtain the Reduced Order Model.
The ROM is tested on a simple configuration that consists of a 2D square enclosed cavity with differentially heated walls opposite of each other. The wall temperature boundary conditions are parametrized using a control function method. For this configuration, the control functions are obtained by solving a Laplacian function for temperature. The ROMs are stable, except when the temperature difference between the walls is larger than the case for which the full order solutions, used for the reduced basis construction, are obtained. The accuracy of the reduced order models is assessed against the full order solutions and it is shown that the reduced order model can be used for sensitivity analysis by controlling the non-homogeneous Dirichlet boundary conditions. Finally, the ROM is about 20 times faster than the FOM on a single processor.

Speaker: Ms Kelbij Star (SCK·CEN)
• 16:18
Reduced-Order Modeling (ROM) for MSR multiphysics simulations 3m

A Proper Orthogonal Decomposition based Reduced-Order Model (POD-ROM) is presented for parameterized multiphysics computations of the Molten Salt Fast Reactor (MSFR) concept. The reduced-order model is created using the method of snapshots where the training set is obtained by exercising a Full-Order Model (FOM). The steady state model solves the multi-group diffusion k-eigenvalue equations with moving precursors together with the energy equation. A known, steady state velocity field is assumed throughout the computations. The Discerete Empirical Interpolation Method (DEIM) is used for the efficient coupling of the ROM solvers, while the input parameter space is surveyed using the Improved Distributed Latin Hypercube Sampling (IHS) algorithm.

Speaker: Mr Peter German (Texas A&M University)
• 16:21
Using Lagrangian models in the simulation of water borne infectious diseases 3m

Fish farming is increasingly important as the demand on food supplies grows with the world’s population. Limiting the spread of disease within such farms is vital, as the detection of such diseases calls for immediate eradication of the infected farm. Optimal farm placement from the prediction of disease spread could potentially limit the spread of infections within these farms. Previous attempts at the prediction of disease spread between farms have not considered significant components of the problem. This study combines a population model with a Lagrangian particle tracking model, to simulate the spread of disease particles as they are generated. The model also considers the influence of the cages on the velocity field, which has been neglected by previous studies. An in-house developed code is used to model the spread of the disease. This code incorporated flow fields generated by OPENFoam, taking into consideration the effect of porous fish farms. The main aim of the study is to couple the disease model to data generated by Delft3D-FLOW.

Speaker: Ms Meghan Kennealy (Stellenbosch University)
• 16:24
Hybrid ROMs for problems in computational fluid dynamics 3m

In this work, we present a hybrid approach for the reduction of fluid dynamics flows. The approach proposed is based on mixing the traditional projection Galerkin methods with data-driven techniques. The goal is to reduce complex problems in CFD with special focus on turbulent flows. The data-driven techniques are utilized in approximating certain fluid dynamics variables in the reduced dynamical system which resulted from a Galerkin projection.

Speaker: Mr Saddam N Y Hijazi (PhD student)
• 16:27
Finite Volume Reduced Order Methods based on SIMPLE Algorithm 3m

In these last months we have been working on the resolution of the parametrized Navier Stokes problem.
In order to apply a reduction method, we started from full order solutions obtained by the use of the OpenFOAM package.
What is new in our work is the effort to follow the SIMPLE algorithm strategy, used in the OpenFOAM full order solvers, also for the reduced problem. The goal is to have a reduced problem as consistent as possible with respect to the full order one.
In this poster the obtained results will be presented, giving a perspective also on future developments.

Speaker: Mr Matteo Zancanaro (SISSA Mathlab)
• 16:30
The polluted atmosphere as a shallow domain 3m

Considered as a geophysical fluid, the polluted atmosphere shares the shallow domain characteristics with other natural large-scale fluids such as seas and oceans. This means that its domain is excessively greater horizontally than in the vertical dimension, leading to the classic hydrostatic approximation of the Navier-Stokes equations. We consider the so-called anisotropic model as a starting point, i.e. a set of equations that describe the atmosphere including the effects of pollution, where the fluid velocity function governed by the classical Navier-Stokes equations is combined with a concentration function representing the pollution. We provide a convergence theorem for the weak solutions of the anisotropic model towards the hydrostatic system. Our results are valid on local domains where the use of Cartesian coordinates are legitimate and effects such as the curvature of the Earth are negligible. The shallow domain concept of the atmosphere is grasped by the small variable $\epsilon$ which stands for the aspect ratio, i.e. the ratio of the characteristic depth and characteristic width. We explicitly involve this aspect ratio in the coordinates and variables that describe the phenomena, then perform a rescaling process according to the "almost two-dimensional" concept we use that makes the domain independent of $\epsilon$. The main two models between which we describe the convergence result are the original anisotropic model and the hydrostatic limit model. In the first one we use the Navier-Stokes equations in all three space dimensions to describe the fluid velocity, while in the latter model we arrive to a simpler equation in the vertical dimension, namely we see the hydrostatic approximation incorporated into the model. The main steps of the proof for the convergence result between the two models are a) using the classical method of extracting a priori bounds from the energy inequality, b) passing to the limit in the linear terms, and, finally, c) using a compactness result that allows us to pass to the limit in the nonlinear terms that require stronger regularities. The visualisation of this convergence result using the finite element method is challenging as a result of the disappearing control over the vertical velocity: the matrix of the anisotropic system becomes more and more badly conditioned as the weight of the vertical velocity is decreasing with $\epsilon$ from the vertical momentum equation.

Joint work with: D. Donatelli, University of L'Aquila

Speaker: Ms Nora Juhasz (University of L'Aquila)
• 16:33
Reduced Order Methods for Boundary Conditions Estimation 3m

In continuous casting machinery, the molten metal solidifies in a mold. In order to control the casting process, a proper knowledge of the heat flux between the mold and the metal is crucial. This boundary condition can be estimated using thermocouples measurements inside the mold and solving an inverse problem. In this research we exploit model order reduction techniques to achieve an online solution of this problem.

Speaker: Mr Umberto Morelli (ITMATI)
• 16:36
Reduced Basis Method: The Smagorinsky Model 3m

We are interested in the design of eco-efficient buildings. This involves computing models for several parameters which could be geometrical or physical. Sometimes, each computation could take a long time and this situation is not the most desirable. This reason encourages us to consider the basis reduced method that allow us to obtain a faster solution with a little error.

Speaker: Ms Cristina Caravaca García (Universidad de sevilla)
• 16:39
Reduction in parameter space with non linear active subspaces 3m

Dimension reduction techniques confer benefits to parametric studies in a great number of engineering applications. Active subspaces proposed by Trent Russi and developed by Paul Constantine have proven to be a versatile method in this matter for models with an underneath linear trend. Some efforts are directed to possible non-linear extensions. The turning point may come from machine learning non-linear supervised dimensionality reduction theory with a focus on supervised kernel principal component analysis and its randomized variant with Random Fourier Features. As testing ground for these possible improvements we present some test cases involving hypersurfaces of revolution with different generatrices.

Speaker: Mr Francesco Romor (SISSA)
• 16:42
Reduced Order Methods Applied to Nonlinear Time Dependent Optimal Flow Control Problems in Environmental Marine Sciences and Engineering 3m

Optimal flow control problems governed by parametrized partial differential equations are a very powerful mathematical model. They are suitable to describe several complex physical phenomena and they are quite spread in different applications. Although, the computational effort increases when one has to deal with nonlinear and/or time dependent governing equations [3,4,5].
We propose reduced order methods as an effective strategy to solve them in a fast and accurate way.
We applied our methodology in environmental marine sciences and engineering where parametrized optimal flow control is really useful to describe different parametric configurations which reliably reproduce physical phenomena. Since these adaptive simulations are very demanding and costly.
We exploit a POD-Galerkin reduction of the optimality system both for the linear and for the nonlinear case in order to save computational time. Two environmental applications are presented [3]: a pollutant control in the Gulf of Trieste, Italy and a solution tracking governed by nonlinear quasi-geostrophic equations describing nonlinear North Atlantic Ocean dynamic. Finally, we propose a parametrized reduced version of time dependent optimal control problems presented in [1,2]: we will show how reduce order methods are advantageous to this more complex context [4].

[1] M. Stoll and A. J. Wathen, "All-at-once solution of time-dependent PDE-constrained optimization problems", Technical Report, 2010.
[2] M. Stoll and A. J. Wathen, "All-at-once solution of time-dependent Stokes control", J. Comput. Phys., 232(1), pp. 498 - 515, 2013.
[3] M. Strazzullo, F. Ballarin, R. Mosetti, and G. Rozza, “Model
Reduction for Parametrized Optimal Control Problems in Environmental
Marine Sciences and Engineering”, SIAM Journal on Scientific
Computing
, 40(4), pp. B1055-B1079, 2018
[4] M. Strazzullo, F. Ballarin, and G. Rozza, "POD-Galerkin based Model Order Reduction for Parametrized Time Dependent Linear Quadratic Optimal Control Problems”. In preparation,
[5] Z. Zainib, M. Strazzullo, F. Ballarin and G. Rozza, "Reduced order methods for parametrized nonlinear and time dependent optimal flow control problems: applications in biomedical and environmental marine sciences". In preparation.

Speaker: Ms Maria Strazzullo (SISSA, mathlab)
• 16:45
Enriched Galerkin Discretization for Mixed-Dimensional Modelling Flow in Fractured Porous Media 3m

This paper presents the enriched Galerkin discretization for modelling fluid flow in fractured porous media using the mixed-dimensional approach. The block structure used to compose this mixed-dimensional problem is presented. The proposed method has been tested against published benchmarks. Moreover, the heterogeneous matrix permeability setting is utilized to assess the enriched Galerkin performance in handling the discontinuity within the matrix domain and between the matrix and fracture domains. Our results illustrate that the enriched Galerkin method has the same advantages as discontinuous Galerkin method; for example, conserves local and global fluid mass, captures the pressure discontinuity, and provides the optimal error convergence rate. However, the enriched Galerkin method requires much fewer degrees of freedom than the discontinuous Galerkin method. The pressure solutions produced by both methods are approximately similar regardless of the conductive or non-conductive fractures or heterogeneity in bulk matrix permeability input.

• 16:48
Reduced order methods for parametric optimal flow control in patient-specific coronary bypass grafts: geometrical reconstruction, data assimilation 3m

In this work, we will present implementation of reduced order methods for parametrized problems in computational fluid dynamics, with a special attention to inverse problems, such as optimal flow control problems and data assimilation in biomedical sciences.

Our focus will, specifically, be on minimizing the misfit between clinical measurements acquired in coronary artery bypass graft surgery and the related variables recovered through computational fluid dynamics. In this framework, the unknown control provides an opportunity to quantify the boundary conditions in computational hemodynamics modeling, specifically for hard-to-quantify outflow conditions. Furthermore, in this work, we adjoin the parametrized optimal flow control paradigm with reduced order methods (ROMs), such as proper orthogonal decomposition (POD)-Galerkin, to solve such many-query parameter dependent problems in a time-efficient manner.

Speaker: Ms Zakia Zainib (mathLab, Mathematics Area, SISSA International School for Advanced Studies, Trieste, Italy)
• 17:30 18:30
Aperitif 1h
• Thursday, 11 July
• 09:00 09:45
Spectral Element Method for Computational Fluid Dynamics 45m
Speaker: Dr Martin Hess (SISSA)
• 09:45 10:30
Guest Lecture - Prof. Annalisa Quaini - Reduced-Order Modeling for PDEs with bifurcating solutions: applications in CFD 45m
Speaker: Prof. Annalisa Quaini
• 10:30 11:00
Coffe Break with Group Picture 30m
• 11:00 11:45
Reduced Order Models for Fluid Structure Interaction 45m
Speaker: Prof. Gianluigi Rozza (Full professor)
• 11:45 12:30
Non-Intrusive Reduced Order Models for CFD 45m
Speaker: Marco Tezzele (SISSA)
• 12:30 14:00
Lunch Break 1h 30m
• 14:00 14:45
Practical Session with ITHACA-FV 45m
Speaker: Dr Giovanni Stabile
• 14:45 15:30
Practical Session with ITHACA-FV 45m
Speaker: Dr Giovanni Stabile
• 15:30 16:00
Coffe Break 30m
• 16:00 16:45
Stabilization for convection dominated problems 45m
• 16:45 17:30
Introduction to the Discontinuous Galerkin Method and to compressible flows 45m
Speaker: Dr Andrea Lario
• 17:30 18:15
Reduced Basis for Embedded Methods 45m
Speaker: Dr Efthymios Karatzas (SISSA)
• 20:00 21:30
Dinner In Trieste 1h 30m
• Friday, 12 July
• 09:00 09:45
Reduction in the parameter space 45m
Speaker: Marco Tezzele (SISSA)
• 09:45 10:30
Python Companion packages for preprocessing 45m
Speaker: Nicola Demo (MHPC)
• 10:30 11:00
coffe break 30m
• 11:00 11:45
Model Reduction for Industrial Applications 45m
Speaker: Dr Andrea Mola (SISSA)
• 11:45 12:30
Guest Lecture - Prof. Simona Perotto - HiMOD methods for Computational Fluid Dynamics 45m
Speaker: Prof. Simona Perotto (MOX, Department of Mathematics, Politecnico di Milano)
• 12:30 13:15
Guest Lecture - Dr. Matteo Giacomini - The proper generalized decomposition: from low to high-order surrogate models in CFD 45m
Speaker: Dr Matteo Giacomini (Universitat Politècnica de Catalunya)
• 13:15 13:30
Conclusion 15m
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