Approximating the trajectory attractor of the 3D Navier-Stokes system using various $ \alpha$-models of fluid dynamics

2016 ◽  
Vol 207 (4) ◽  
pp. 610-638
Author(s):  
V V Chepyzhov
Keyword(s):  
Fluid Dynamics ◽  
Stokes System ◽  
Navier Stokes ◽  
Trajectory Attractor ◽  
Alpha Models

scholarly journals Trajectory statistical solutions for the Cahn-Hilliard-Navier-Stokes system with moving contact lines

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Bo You
Keyword(s):  
Stokes System ◽  
Two Dimensions ◽  
Navier Stokes ◽  
Time Behavior ◽  
Contact Lines ◽  
Trajectory Attractor ◽  
Moving Contact ◽  
Moving Contact Lines ◽  
Long Time ◽  
Statistical Solutions

<p style='text-indent:20px;'>The objective of this paper is to consider the long-time behavior of solutions for the Cahn-Hilliard-Navier-Stokes system with moving contact lines. As we know, it is very difficult to obtain the uniqueness of an energy solution for this system even in two dimensions caused by the presence of the strong coupling at the boundary. Thus, we first prove the existence of a trajectory attractor for such system, which is a minimal compact trajectory attracting set for the natural translation semigroup defined on the trajectory space. Furthermore, based on the abstract results (trajectory attractor approach) developed in [<xref ref-type="bibr" rid="b38">38</xref>], we construct trajectory statistical solutions for the Cahn-Hilliard-Navier-Stokes system with moving contact lines.</p>

scholarly journals Some preliminary observations on a defect Navier–Stokes system

2019 ◽  
Vol 347 (10) ◽  
pp. 677-684 ◽  
Author(s):  
Amit Acharya ◽  
Roger Fosdick
Keyword(s):  
Stokes System ◽  
Navier Stokes

scholarly journals Detailed Modeling of Cork-Phenolic Ablators in Preparation for the Post-flight Analysis of the QARMAN Re-entry CubeSat

2021 ◽  
Author(s):  
Claudio Miccoli ◽  
Alessandro Turchi ◽  
Pierre Schrooyen ◽  
Domenic D’Ambrosio ◽  
Thierry Magin
Keyword(s):  
Fluid Dynamics ◽  
Thermal Protection ◽  
A Priori ◽  
European Space Agency ◽  
Thermal Response ◽  
Accurate Method ◽  
Navier Stokes ◽  
Advection Equation ◽  
High Enthalpy ◽  
Space Agency

AbstractThis work deals with the analysis of the cork P50, an ablative thermal protection material (TPM) used for the heat shield of the qarman Re-entry CubeSat. Developed for the European Space Agency (ESA) at the von Karman Institute (VKI) for Fluid Dynamics, qarman is a scientific demonstrator for Aerothermodynamic Research. The ability to model and predict the atypical behavior of the new cork-based materials is considered a critical research topic. Therefore, this work is motivated by the need to develop a numerical model able to respond to this demand, in preparation to the post-flight analysis of qarman. This study is focused on the main thermal response phenomena of the cork P50: pyrolysis and swelling. Pyrolysis was analyzed by means of the multi-physics Computational Fluid Dynamics (CFD) code argo, developed at Cenaero. Based on a unified flow-material solver, the Volume Averaged Navier–Stokes (VANS) equations were numerically solved to describe the interaction between a multi-species high enthalpy flow and a reactive porous medium, by means of a high-order Discontinuous Galerkin Method (DGM). Specifically, an accurate method to compute the pyrolysis production rate was implemented. The modeling of swelling was the most ambitious task, requiring the development of a physical model accounting for this phenomenon, for the purpose of a future implementation within argo. A 1D model was proposed, mainly based on an a priori assumption on the swelling velocity and the resolution of a nonlinear advection equation, by means of a Finite Difference Method (FDM). Once developed, the model was successfully tested through a matlab code, showing that the approach is promising and thus opening the way to further developments.

scholarly journals Asymptotic analysis of an optimal control problem for a viscous incompressible fluid with Navier slip boundary conditions

2021 ◽  
pp. 1-21
Author(s):  
Claudia Gariboldi ◽  
Takéo Takahashi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Stokes System ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Slip ◽  
Slip Boundary ◽  
Navier Slip Boundary Conditions

We consider an optimal control problem for the Navier–Stokes system with Navier slip boundary conditions. We denote by α the friction coefficient and we analyze the asymptotic behavior of such a problem as α → ∞. More precisely, we prove that if we take an optimal control for each α, then there exists a sequence of optimal controls converging to an optimal control of the same optimal control problem for the Navier–Stokes system with the Dirichlet boundary condition. We also show the convergence of the corresponding direct and adjoint states.

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