相关论文: Nonlinear model reduction: a comparison between PO…

This study investigates the generalization capabilities and robustness of purely deep learning (DL) models and hybrid models based on physical principles in fluid dynamics applications, specifically focusing on iteratively forecasting the…

We consider proper orthogonal decomposition (POD) methods to approximate the incompressible Navier-Stokes equations. We study the case in which one discretization for the nonlinear term is used in the snapshots (that are computed with a…

The paper studies parametric Reduced Order Models (ROMs) for the Kuramoto--Sivashinsky (KS) and generalized Kuramoto--Sivashinsky (gKS) equations. We consider several POD and POD-DEIM projection ROMs with various strategies for parameter…

In this work we recast parametrized time dependent optimal control problems governed by partial differential equations in a saddle point formulation and we propose reduced order methods as an effective strategy to solve them. Indeed, on one…

A methodology for non-intrusive, projection-based non-linear model reduction originally presented by Renganathan et. al. (2018)~\cite{renganathan2018koopman} is further extended towards parametric systems with focus on application to…

We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration…

Computational fluid dynamics (CFD) simulations play an important role in engineering science and applications, however, it is not applicable for problems requiring a large number of repeated calculations. Accordingly, many reduced-order…

Plasmas are highly nonlinear and multi-scale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD), although these…

This paper focuses on a new framework for reduced order modelling of non-intrusive data with application to 2D flows. To overcome the shortcomings of intrusive model order reduction usually derived by combining the POD and the Galerkin…

The purpose of this work is to present a reduced order modeling framework for parametrized turbulent flows with moderately high Reynolds numbers within the variational multiscale (VMS) method. The Reduced Order Models (ROMs) presented in…

State-specific thermochemical collisional models are crucial to accurately describe the physics of systems involving nonequilibrium plasmas, but they are also computationally expensive and impractical for large-scale, multi-dimensional…

We investigate linear-quadratic dynamical systems with energy preserving quadratic terms. These systems arise for instance as Galerkin systems of incompressible flows. A criterion is presented to ensure long-term boundedness of the system…

In the present paper we consider a 2-D shallow-water equations (SWE) model on a $\beta$-plane solved using an alternating direction fully implicit (ADI) finite-difference scheme on a rectangular domain. The scheme was shown to be…

In feedback flow control, one of the challenges is to develop mathematical models that describe the fluid physics relevant to the task at hand, while neglecting irrelevant details of the flow in order to remain computationally tractable. A…

The purpose of the present paper is to compare two semi-Lagrangian methods in the context of the four-dimensional Vlasov--Poisson equation. More specifically, our goal is to compare the performance of the more recently developed…

We present a high-order implicit large eddy simulation (ILES) approach for simulating flows at the nearly incompressible regime. Our methodology based on utilization of a nodal discontinuous Galerkin (DG) discretization of the Boltzmann…

This article revisits the approximation problem of systems of nonlinear delay differential equations (DDEs) by a set of ordinary differential equations (ODEs). We work in Hilbert spaces endowed with a natural inner product including a point…

In this study, we explore the effect of basis functions on the performance and convergence of the Galerkin projection-based reduced-order model (ROM) in the minimal flow unit of Couette flow. POD (proper orthogonal decomposition) modes…

Some hyperbolic systems are known to include implicit preservation of differential constraints: these are for example the time conservation of the curl or the divergence of a vector that appear as an implicit constraint. In this article, we…

Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing…