16 research outputs found
A reduced order variational multiscale approach for turbulent flows
The purpose of this work is to present different reduced order model strategies starting from full order simulations stabilized using a residual-based variational multiscale (VMS) approach. The focus is on flows with moderately high Reynolds numbers. The reduced order models (ROMs) presented in this manuscript are based on a POD-Galerkin approach. Two different reduced order models are presented, which differ on the stabilization used during the Galerkin projection. In the first case, the VMS stabilization method is used at both the full order and the reduced order levels. In the second case, the VMS stabilization is used only at the full order level, while the projection of the standard Navier-Stokes equations is performed instead at the reduced order level. The former method is denoted as consistent ROM, while the latter is named non-consistent ROM, in order to underline the different choices made at the two levels. Particular attention is also devoted to the role of inf-sup stabilization by means of supremizers in ROMs based on a VMS formulation. Finally, the developed methods are tested on a numerical benchmark. © 2019, Springer Science+Business Media, LLC, part of Springer Nature
Variational multiscale reinforcement learning for discovering reduced order closure models of nonlinear spatiotemporal transport systems
A central challenge in the computational modeling and simulation of a multitude of science applications is to achieve robust and accurate closures for their coarse-grained representations due to underlying highly nonlinear multiscale interactions. These closure models are common in many nonlinear spatiotemporal systems to account for losses due to reduced order representations, including many transport phenomena in fluids. Previous data-driven closure modeling efforts have mostly focused on supervised learning approaches using high fidelity simulation data. On the other hand, reinforcement learning (RL) is a powerful yet relatively uncharted method in spatiotemporally extended systems. In this study, we put forth a modular dynamic closure modeling and discovery framework to stabilize the Galerkin projection based reduced order models that may arise in many nonlinear spatiotemporal dynamical systems with quadratic nonlinearity. However, a key element in creating a robust RL agent is to introduce a feasible reward function, which can be constituted of any difference metrics between the RL model and high fidelity simulation data. First, we introduce a multi-modal RL to discover mode-dependant closure policies that utilize the high fidelity data in rewarding our RL agent. We then formulate a variational multiscale RL (VMRL) approach to discover closure models without requiring access to the high fidelity data in designing the reward function. Specifically, our chief innovation is to leverage variational multiscale formalism to quantify the difference between modal interactions in Galerkin systems. Our results in simulating the viscous Burgers equation indicate that the proposed VMRL method leads to robust and accurate closure parameterizations, and it may potentially be used to discover scale-aware closure models for complex dynamical systems.publishedVersio
A Reduced basis stabilization for the unsteady Stokes and Navier-Stokes equations
In the Reduced Basis approximation of Stokes and Navier-Stokes problems, the
Galerkin projection on the reduced spaces does not necessarily preserved the
inf-sup stability even if the snapshots were generated through a stable full
order method. Therefore, in this work we aim at building a stabilized Reduced
Basis (RB) method for the approximation of unsteady Stokes and Navier-Stokes
problems in parametric reduced order settings. This work extends the results
presented for parametrized steady Stokes and Navier-Stokes problems in a work
of ours \cite{Ali2018}. We apply classical residual-based stabilization
techniques for finite element methods in full order, and then the RB method is
introduced as Galerkin projection onto RB space. We compare this approach with
supremizer enrichment options through several numerical experiments. We are
interested to (numerically) guarantee the parametrized reduced inf-sup
condition and to reduce the online computational costs.Comment: arXiv admin note: text overlap with arXiv:2001.0082
Projection-based reduced order models for a cut finite element method in parametrized domains
This work presents a reduced order modeling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order models thanks to their capabilities to seamlessly handle large deformations of parametrized domains and in general to handle topological changes. The combination of embedded methods and reduced order models allows us to obtain fast evaluation of parametrized problems, avoiding remeshing as well as the reference domain formulation, often used in the reduced order modeling for boundary fitted finite element formulations. The resulting novel methodology is presented on linear elliptic and Stokes problems, together with several test cases to assess its capability. The role of a proper extension and transport of embedded solutions to a common background is analyzed in detail. \ua9 2019 Elsevier Lt
A POD-Galerkin reduced order model of a turbulent convective buoyant flow of sodium over a backward-facing step
A Finite-Volume based POD-Galerkin reduced order modeling strategy for
steady-state Reynolds averaged Navier--Stokes (RANS) simulation is extended for
low-Prandtl number flow. The reduced order model is based on a full order model
for which the effects of buoyancy on the flow and heat transfer are
characterized by varying the Richardson number. The Reynolds stresses are
computed with a linear eddy viscosity model. A single gradient diffusion
hypothesis, together with a local correlation for the evaluation of the
turbulent Prandtl number, is used to model the turbulent heat fluxes. The
contribution of the eddy viscosity and turbulent thermal diffusivity fields are
considered in the reduced order model with an interpolation based data-driven
method. The reduced order model is tested for buoyancy-aided turbulent liquid
sodium flow over a vertical backward-facing step with a uniform heat flux
applied on the wall downstream of the step. The wall heat flux is incorporated
with a Neumann boundary condition in both the full order model and the reduced
order model. The velocity and temperature profiles predicted with the reduced
order model for the same and new Richardson numbers inside the range of
parameter values are in good agreement with the RANS simulations. Also, the
local Stanton number and skin friction distribution at the heated wall are
qualitatively well captured. Finally, the reduced order simulations, performed
on a single core, are about times faster than the RANS simulations that
are performed on eight cores.Comment: 26 pages, 15 figures, 3 table
Predictive Reduced Order Modeling of Chaotic Multi-scale Problems Using Adaptively Sampled Projections
An adaptive projection-based reduced-order model (ROM) formulation is
presented for model-order reduction of problems featuring chaotic and
convection-dominant physics. An efficient method is formulated to adapt the
basis at every time-step of the on-line execution to account for the unresolved
dynamics. The adaptive ROM is formulated in a Least-Squares setting using a
variable transformation to promote stability and robustness. An efficient
strategy is developed to incorporate non-local information in the basis
adaptation, significantly enhancing the predictive capabilities of the
resulting ROMs. A detailed analysis of the computational complexity is
presented, and validated. The adaptive ROM formulation is shown to require
negligible offline training and naturally enables both future-state and
parametric predictions. The formulation is evaluated on representative reacting
flow benchmark problems, demonstrating that the ROMs are capable of providing
efficient and accurate predictions including those involving significant
changes in dynamics due to parametric variations, and transient phenomena. A
key contribution of this work is the development and demonstration of a
comprehensive ROM formulation that targets predictive capability in chaotic,
multi-scale, and transport-dominated problems
Consistency of the full and reduced order models for evolve-filter-relax regularization of convection-dominated, marginally-resolved flows
Numerical stabilization is often used to eliminate (alleviate) the spurious oscillations generally produced by full order models (FOMs) in under-resolved or marginally-resolved simulations of convection-dominated flows. In this article, we investigate the role of numerical stabilization in reduced order models (ROMs) of marginally-resolved, convection-dominated incompressible flows. Specifically, we investigate the FOM–ROM consistency, that is, whether the numerical stabilization is beneficial both at the FOM and the ROM level. As a numerical stabilization strategy, we focus on the evolve-filter-relax (EFR) regularization algorithm, which centers around spatial filtering. To investigate the FOM-ROM consistency, we consider two ROM strategies: (i) the EFR-noEFR, in which the EFR stabilization is used at the FOM level, but not at the ROM level; and (ii) the EFR-EFR, in which the EFR stabilization is used both at the FOM and at the ROM level. We compare the EFR-noEFR with the EFR-EFR in the numerical simulation of a 2D incompressible flow past a circular cylinder in the convection-dominated, marginally-resolved regime. We also perform model reduction with respect to both time and Reynolds number. Our numerical investigation shows that the EFR-EFR is more accurate than the EFR-noEFR, which suggests that FOM-ROM consistency is beneficial in convection-dominated, marginally-resolved flows