01828nas a2200241 4500008004100000022001400041245013800055210007300193300001200266490000800278520099800286653003301284653002501317653002001342653001301362653003601375653002801411100001701439700001801456700001901474700002101493856007201514 2024 eng d a0898-122100aAn optimisation–based domain–decomposition reduced order model for parameter–dependent non–stationary fluid dynamics problems0 aoptimisation–based domain–decomposition reduced order model for  a253-2680 v1663 a

In this work, we address parametric non–stationary fluid dynamics problems within a model order reduction setting based on domain decomposition. Starting from the optimisation–based domain decomposition approach, we derive an optimal control problem, for which we present a convergence analysis in the case of non–stationary incompressible Navier–Stokes equations. We discretise the problem with the finite element method and we compare different model order reduction techniques: POD–Galerkin and a non–intrusive neural network procedures. We show that the classical POD–Galerkin is more robust and accurate also in transient areas, while the neural network can obtain simulations very quickly though being less precise in the presence of discontinuities in time or parameter domain. We test the proposed methodologies on two fluid dynamics benchmarks with physical parameters and time dependency: the non–stationary backward–facing step and lid–driven cavity flow.

10aComputational fluid dynamics10aDomain decomposition10aOptimal control10aPOD–NN10aProper orthogonal decomposition10aReduced order modelling1 aPrusak, Ivan1 aTorlo, Davide1 aNonino, Monica1 aRozza, Gianluigi uhttps://www.sciencedirect.com/science/article/pii/S089812212400209802085nas a2200253 4500008004100000020001400041245011800055210007300173260001600246300001400262490000800276520123400284653003301518653002501551653002001576653003601596653002801632100001701660700001901677700001801696700002401714700002101738856007201759 2023 eng d a0898-122100aAn optimisation–based domain–decomposition reduced order model for the incompressible Navier-Stokes equations0 aoptimisation–based domain–decomposition reduced order model for  c2023/12/01/ a172 - 1890 v1513 a

The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical models: domain–decomposition (DD) methods and reduced–order modelling (ROM). In particular, we consider an optimisation–based domain–decomposition algorithm for the parameter–dependent stationary incompressible Navier–Stokes equations. Firstly, the problem is described on the subdomains coupled at the interface and solved through an optimal control problem, which leads to the complete separation of the subdomain problems in the DD method. On top of that, a reduced model for the obtained optimal–control problem is built; the procedure is based on the Proper Orthogonal Decomposition technique and a further Galerkin projection. The presented methodology is tested on two fluid dynamics benchmarks: the stationary backward–facing step and lid-driven cavity flow. The numerical tests show a significant reduction of the computational costs in terms of both the problem dimensions and the number of optimisation iterations in the domain–decomposition algorithm.

10aComputational fluid dynamics10aDomain decomposition10aOptimal control10aProper orthogonal decomposition10aReduced order modelling1 aPrusak, Ivan1 aNonino, Monica1 aTorlo, Davide1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.sciencedirect.com/science/article/pii/S089812212300424802038nas a2200217 4500008004100000022001400041245010200055210006900157490003500226520122900261653002501490653002101515653002501536653002701561653002501588653001601613100002201629700002101651700002201672856012601694 2015 eng d a1019-716800aReduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system0 aReduced basis approximation and aposteriori error estimation for0 vspecial issue for MoRePaS 20123 a

The coupling of a free flow with a flow through porous media has many potential applications in several fields related with computational science and engineering, such as blood flows, environmental problems or food technologies. We present a reduced basis method for such coupled problems. The reduced basis method is a model order reduction method applied in the context of parametrized systems. Our approach is based on a heterogeneous domain decomposition formulation, namely the Stokes-Darcy problem. Thanks to an offline/online-decomposition, computational times can be drastically reduced. At the same time the induced error can be bounded by fast evaluable a-posteriori error bounds. In the offline-phase the proposed algorithms make use of the decomposed problem structure. Rigorous a-posteriori error bounds are developed, indicating the accuracy of certain lifting operators used in the offline-phase as well as the accuracy of the reduced coupled system. Also, a strategy separately bounding pressure and velocity errors is extended. Numerical experiments dealing with groundwater flow scenarios demonstrate the efficiency of the approach as well as the limitations regarding a-posteriori error estimation.

10aDomain decomposition10aError estimation10aNon-coercive problem10aPorous medium equation10aReduced basis method10aStokes flow1 aMartini, Immanuel1 aRozza, Gianluigi1 aHaasdonk, Bernard uhttps://math.sissa.it/publication/reduced-basis-approximation-and-posteriori-error-estimation-coupled-stokes-darcy-system