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Robust Controller versus Numerical Model Uncertainties for Stabilization of Navier-Stokes Equations
2019
IFAC-PapersOnLine
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In numerical experiments, we quantify the robustness margins and show that the H ∞ -robust controller, unlike the LQGcontroller, is capable of stabilizing nonlinear incompressible Navier-Stokes equations ...
In numerical experiments, we quantify the robustness margins and show that the H ∞ -robust controller, unlike the LQGcontroller, is capable of stabilizing nonlinear incompressible Navier-Stokes equations ...
In numerical experiments, we quantify the robustness margins and show that the H ∞ -robust controller, unlike the LQGcontroller, is capable of stabilizing nonlinear incompressible Navier-Stokes equations ...
doi:10.1016/j.ifacol.2019.08.005
fatcat:y4xbshdtmjax5n4xpnvmx3srwq
Reduction of Asymptotic Approximate Expansion of Navier–Stokes Equation and Solution of Inviscid Burgers Equation by Similarity Transformation
2021
Scientific Programming
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Particularly, we will apply this transformation to the nonlinear Navier–Stokes partial differential equations to reduce them to ordinary differential equations. ...
It linearizes nonlinear differential equations, reduces the order of differential equations, reduces the number of independent variables in partial differential equations, and solves almost all those differential ...
Conflicts of Interest e authors declare that they have no conflicts of interest to report regarding the present study. ...
doi:10.1155/2021/9054328
fatcat:qlucwgbyanambgldhjj4e6mhva
Page 5826 of Mathematical Reviews Vol. , Issue 2000h
[page]
2000
Mathematical Reviews
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The flow evolution, as described by the nonlinear model, shows agreement with time history plots from simulations using the unsteady Navier-Stokes equations. ...
Instead of the Navier-Stokes equations we consider one nonlinear Helmholtz equation for the stream func- tion. The Newton polyhedron of the Helmholtz equation is a trapezoid. ...
A Bayesian Nonlinear Reduced Order Modeling Using Variational AutoEncoders
2022
Fluids
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This paper presents a new nonlinear projection based model reduction using convolutional Variational AutoEncoders (VAEs). This framework is applied on transient incompressible flows. ...
The parameters of the nonlinear manifold are optimized as the ones of the decoder layers of an autoencoder. ...
It is based on applying the model reduction on the time-discretized incompressible and unsteady Navier-Stokes equations. ...
doi:10.3390/fluids7100334
fatcat:apawwglbtvhwdfyu522qqzv5zy
Multiscale model reduction technique for fluid flows with heterogeneous porous inclusions
[article]
2022
arXiv
pre-print
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The mathematical model is described by Navier-Stokes equation in the free flow domain Ω_f and nonlinear convective Darcy-Brinkman-Forchheimer equations in porous subdomains Ω_p. ...
The size alteration of the relevant system requires model reduction techniques. ...
We consider Navier-Stokes equations in the exterior flow domain (clear fluid domain) and Darcy-Brinkman-Forchheimer model equations in the porous subdomains and solve the boundary value problem numerically ...
arXiv:2209.01155v1
fatcat:zcu47lq5zfbajidyabjhjiolsy
Nonlinear estimation of fluid flow velocity fields
2011
IEEE Conference on Decision and Control and European Control Conference
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Using Galerkin projection and POD-based model reduction, the incompressible Navier-Stokes equations are recast as a set of nonlinear ordinary differential equations in the Galerkin coefficients. ...
A proper orthogonal decomposition (POD)-based nonlinear estimator for fluid flow velocity fields is developed, which is capable of achieving finite-time convergence of the Galerkin coefficient estimates ...
To this end, PODbased model reduction will be utilized to express the incompressible Navier-Stokes equations as a set of nonlinear ordinary differential equations. ...
doi:10.1109/cdc.2011.6161193
dblp:conf/cdc/MacKunisDRU11
fatcat:spuocp4cl5f5ddmewznhwurfw4
Page 5534 of Mathematical Reviews Vol. , Issue 89J
[page]
1989
Mathematical Reviews
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Summary: “In this note we present an explicit nonlinear approxi- mating manifold for the universal (global) attractor of the Navier- Stokes equations, of finite dimension m. ...
Reduction and exact solutions of five-dimensional nonlinear wave equations. (Russian)
Akad. Nauk Ukrain. SSR Inst. Mat. Preprint 1988, no. 21, 28 pp. ...
Finite element approximations of the Navier-Stokes equations
1981
Applied Mathematical Modelling
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An APL function for the approximation of multiplier values in system dynamics models a research note by me appeared entitled: 'simulating system dynamics in APL'. T. Bratano w ...
Chapter 4 presents the stationary Navier-Stokes equations, a discussion of a class of nonlinear problems, the application to the Navier-Stokes equations as well as a method for approximation of these equations ...
This nonlinear theory is then applied to the solution of stationary Navier-Stokes equations with proposed finite element approximation of the problem in two dimensions. ...
doi:10.1016/0307-904x(81)90049-4
fatcat:mbrmojsvcfetdazvjduoxk42dq
Page 8739 of Mathematical Reviews Vol. , Issue 99m
[page]
1999
Mathematical Reviews
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algorithm for the Navier-Stokes equations. ...
element method for the three- dimensional unsteady Navier-Stokes equation. ...
Modeling 3-D compliant blood flow with FOSLS
2004
Biomedical sciences instrumentation
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Blood flow in large vessels is typically modeled using the Navier-Stokes equations for the fluid domain and elasticity equations for the vessel wall. ...
As the wall deforms, additional complications are introduced because the shape of the fluid domain changes, necessitating the use of a re-mapping or re-griding process for the fluid region. ...
Further, despite the fact that both the Navier-Stokes and EGG equations are nonlinear, a stable solution was found with only a single linearization step (i.e., Newton step) each time the equations were ...
pmid:15133957
fatcat:5jjjgznxabem7ofye4yyg23b74
Page 2986 of Mathematical Reviews Vol. , Issue 2004d
[page]
2004
Mathematical Reviews
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of solutions to the Navier-Stokes equations. ...
First the author gives a short overview of related results, including one of He about the regularity of the Navier-Stokes equations provided Vu; € L'(I; L), 24 : ret MONS t <0, 3<s <0, where L'(J; L*) ...
HJB-POD feedback control for Navier-Stokes equations
[article]
2014
arXiv
pre-print
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The method is based on a model reduction technique, using a POD approximation, coupled with a Hamilton-Jacobi equation which characterizes the value function of the corresponding control problem for the ...
In this report we present the approximation of an infinite horizon optimal control problem for the evolutive Navier-Stokes system. ...
The novelty in this paper consists in the control of the 2D nonlinear time dependent Navier-Stokes system by means of DP equations and the reduction of the nonlinear term with the Discrete Empirical Interpolation ...
arXiv:1405.1209v1
fatcat:orvrop3p6nc3xgtsekggy2tvri
The Problem of Single – Determinability Equations of Navier-Stokes
2019
International Journal of Mathematics and Physics
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The Navier-Stokes equations describing a viscous incompressible fluid have for many decades attracted the attention of scientists working on the problem of solvability of partial differential equations ...
The theory of the equation of mathematical physics, since, as mentioned above, they are open to the Navier-Stokes system. Therefore, the young scientist S. ...
The method of fictitious areas for the nonlinear Navier-Stokes system. ...
doi:10.26577/ijmph-2019-i1-1
fatcat:sdb4rpieozfppkctqly6xxanby
Optimal Control for Navier-Stokes Takagi-Sugeno Fuzzy Equations Using Simulink
[chapter]
2011
Communications in Computer and Information Science
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The Navier-Stokes equations are investigated along the lines of the theoretically best index reduction by using several discretization schemes. ...
In this paper, the unsteady Navier-Stokes Takagi-Sugeno (T-S) fuzzy equations (UNSTSFEs) are represented as a differential algebraic system of strangeness index one by applying any spatial discretization ...
Acknowledgements: The funding of this work by the UMRG grant (Account No: RG099/10AFR) is gratefully acknowledged. ...
doi:10.1007/978-3-642-19263-0_7
fatcat:7fatu6sc6rcirkmepyiv5rd6xi
Page 4383 of Mathematical Reviews Vol. , Issue 2000f
[page]
2000
Mathematical Reviews
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Summary: “We study similarity reductions and exact solutions of the (2+ 1)-dimensional incompressible Navier-Stokes equations using the direct method originally developed by Clarkson and Kruskal. ...
and exact solutions for the two-dimensional incompressible Navier-Stokes equations. ...
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