相关论文: Numerical Analysis of the Leray Reduced Order Mode…
Linear reduced-order modeling (ROM) simplifies complex simulations by approximating the behavior of a system using a simplified kinematic representation. Typically, ROM is trained on input simulations created with a specific spatial…
Mathematical regularisation of the nonlinear terms in the Navier-Stokes equations provides a systematic approach to deriving subgrid closures for numerical simulations of turbulent flow. By construction, these subgrid closures imply…
For reduced order models (ROMs) of fluid flows, we investigate theoretically and computationally whether differentiation and ROM spatial filtering commute, i.e., whether the commutation error (CE) is nonzero. We study the CE for the…
In systems governed by nonlinear partial differential equations such as fluid flows, the design of state estimators such as Kalman filters relies on a reduced-order model (ROM) that projects the original high-dimensional dynamics onto a…
In this paper, a reduced-order model (ROM) based on the proper orthogonal decomposition and the discrete empirical interpolation method is proposed for efficiently simulating time-fractional partial differential equations (TFPDEs). Both…
We develop a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for the efficient numerical simulation of the parametric Navier-Stokes equations in the stream function-vorticity formulation. Unlike previous…
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…
The numerical treatment of fluid-particle systems is a very challenging problem because of the complex coupling phenomena occurring between the two phases. Although accurate mathematical modelling is available to address this kind of…
The Discrete Ordinates Method (DOM) is the most widely used velocity discretization method for simulating the radiative transport equation. However, the ray effect is a long-standing drawback of DOM. In benchmark tests that exhibit the ray…
Reduced-order modeling is an efficient approach for solving parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space and an online step…
It has recently become common to study many different approximating equations of the Navier-Stokes equation. One of these is the Leray-$\alpha$ equation, which regularizes the Navier-Stokes equation by replacing (in most locations) the…
In this paper, we establish the global well-posedness of stochastic 3D Leray-$\alpha$ model with general fractional dissipation driven by multiplicative noise. This model is the stochastic 3D Navier-Stokes equation regularized through 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…
Depth estimation using a single-photon LiDAR is often solved by a matched filter. It is, however, error-prone in the presence of background noise. A commonly used technique to reject background noise is the rank-ordered mean (ROM) filter…
We present a novel reduced order model (ROM) approach for parameterized time-dependent PDEs based on modern learning. The ROM is suitable for multi-query problems and is nonintrusive. It is divided into two distinct stages: A nonlinear…
We propose a calibrated filtered reduced order model (CF-ROM) framework for the numerical simulation of general nonlinear PDEs that are amenable to reduced order modeling. The novel CF-ROM framework consists of two steps: (i) In the first…
We explore a reduced-order model (ROM) of plane Couette flow with a view to performing turbulence control. The ROM is derived through Galerkin projections of the incompressible Navier-Stokes (NS) system onto a basis composed of…
A One-Dimensional (1D) Reduced-Order Model (ROM) has been developed for a 3D Rayleigh-B\'enard convection system in the turbulent regime with Rayleigh number $\mathrm{Ra}=10^6$. The state vector of the 1D ROM is horizontally averaged…
The Discrete Ordinates Method (DOM) is widely used for velocity discretization in radiative transport simulations. However, DOM tends to exhibit the ray effect when the velocity discretization is not sufficiently refined, a limitation that…
We consider the Navier-Stokes equations in a channel with a narrowing of varying height. The model is discretized with high-order spectral element ansatz functions, resulting in 6372 degrees of freedom. The steady-state snapshot solutions…