相关论文: On the reconstruction of unknown driving forces fr…
Using limited observations of the velocity field of the two-dimensional Navier-Stokes equations, we successfully reconstruct the steady body force that drives the flow. The number of observed data points is less than 10\% of the number of…
This article considers the problem of reconstructing unknown driving forces based on incomplete knowledge of the system and its state. This is studied in both a linear and nonlinear setting that is paradigmatic in geophysical fluid dynamics…
We study incompressible Navier--Stokes flows in~$\R^d$ with small and well localized data and external force~$f$. We establish pointwise estimates for large~$|x|$ of the form \hbox{$c_t|x|^{-d}\le |u(x,t)|\le c'_t|x|^{-d}$}, where $c_t>0$…
The presented research paper illustrates the development of a new methodology to solve 2-dimensional (2D) Navier-Stoke equations, which Pukhnachev proposed through introducing unknown functions in the stream and pressure functions of fluid…
Common efficient schemes for the incompressible Navier-Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or introduce errors near the domain boundaries…
Reduced-order modeling has a long tradition in computational fluid dynamics. The ever-increasing significance of data for the synthesis of low-order models is well reflected in the recent successes of data-driven approaches such as Dynamic…
Conventional mathematical models for simulating incompressible fluid flow problems are based on the Navier-Stokes equations expressed in terms of pressure and velocity. In this context, pressure-velocity coupling is a key issue, and…
In fluid mechanics, a lot of authors have been executing their researches to obtain the analytical solutions of Navier-Stokes equations, even for 3D case of compressible gas flow or 3D case of non-stationary flow of incompressible fluid.…
We study the numerical performance of a continuous data assimilation (downscaling) algorithm, based on ideas from feedback control theory, in the context of the two-dimensional incompressible Navier--Stokes equations. Our model problem is…
In this paper, the convergence of an algorithm for recovering the unknown kinematic viscosity of a two-dimensional incompressible, viscous fluid is studied. The algorithm of interest is a recursive feedback control-based algorithm that…
This report presents a low computational and cognitive complexity, stable, time accurate and adaptive method for the Navier-Stokes equations. The improved method requires a minimally intrusive modification to an existing program based on…
Obtaining system parameters and reconstructing the full flow state from limited velocity observations using conventional fluid dynamics solvers can be prohibitively expensive. Here we employ machine learning algorithms to overcome the…
In this paper the issue of the determination of the fluid pressure in incompressible fluids is addressed, with particular reference to the search of algorithms which permit to advance in time the fluid pressure without actually solving…
This article analyses the assumptions regarding the influence of pressure forces during the calculation of the motion of a Newtonian fluid. The purpose of the analysis is to determine the reasonableness of the assumptions and their impact…
In this article we address flow problems that carry a multiscale character in time. In particular we consider the Navier-Stokes flow in a channel on a fast scale that influences the movement of the boundary which undergoes a deformation on…
We consider the global approximate controllability of the two-dimensional incompressible Navier-Stokes system driven by a physically localized and degenerate force. In other words, the fluid is regulated via four scalar controls that depend…
The goal of this paper is to provide an algorithm that, for any sufficiently localised, divergence-free small initial data, explicitly constructs a localised external force leading to a rapidly dissipative solutions of the Navier-Stokes…
We present a component-based model order reduction procedure to efficiently and accurately solve parameterized incompressible flows governed by the Navier-Stokes equations. Our approach leverages a non-overlapping optimization-based domain…
A few basic, intuitive, properties of the Navier-Stokes system of equations for incompressible fluid flows are discussed in this paper. We present a rephrased interpretation of the Navier-Stokes equation in a space having an arbitrary…
We solve an inverse initial data problem for the incompressible Navier-Stokes system. The objective is to recover the initial velocity and pressure from lateral boundary observations, without assuming that the time-independent body force is…