Maximum Principle and Gradient Estimates for Stationary Solutions of the Navier-Stokes Equations: A Partly Numerical Investigation

2009 ◽  
pp. 253-269
Author(s):  
Robert Finn ◽  
Abderrahim Ouazzi ◽  
Stefan Turek
Keyword(s):  
Maximum Principle ◽  
Numerical Investigation ◽  
Stokes Equations ◽  
Stationary Solutions ◽  
Gradient Estimates ◽  
Navier Stokes ◽  
Navier Stokes Equations

On the Stationary Solutions to 2D g-Navier-Stokes Equations

2016 ◽  
Vol 42 (2) ◽  
pp. 357-367 ◽  
Author(s):  
Dao Trong Quyet ◽  
Nguyen Viet Tuan
Keyword(s):  
Stokes Equations ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations

scholarly journals Disconnected stationary solutions for 3D Kolmogorov flow problem: preliminary results

2021 ◽  
Vol 2090 (1) ◽  
pp. 012046
Author(s):  
Nikolay M. Evstigneev
Keyword(s):  
Flow Problem ◽  
Stokes Equations ◽  
Continuation Method ◽  
Fourier Method ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
System Of Nonlinear Equations ◽  
Arc Length ◽  
Navier Stokes Equations ◽  
Numerical Bifurcation

Abstract The extension of the classical A.N. Kolmogorov’s flow problem for the stationary 3D Navier-Stokes equations on a stretched torus for velocity vector function is considered. A spectral Fourier method with the Leray projection is used to solve the problem numerically. The resulting system of nonlinear equations is used to perform numerical bifurcation analysis. The problem is analyzed by constructing solution curves in the parameter-phase space using previously developed deflated pseudo arc-length continuation method. Disconnected solutions from the main solution branch are found. These results are preliminary and shall be generalized elsewhere.

scholarly journals Finite-Volume Solvers for a Multilayer Saint-Venant System

2007 ◽  
Vol 17 (3) ◽  
pp. 311-320 ◽  
Author(s):  
Emmanuel Audusse ◽  
Marie-Odile Bristeau
Keyword(s):  
Shallow Water ◽  
Numerical Investigation ◽  
Finite Volume ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Relevant Alternative ◽  
Navier Stokes Equations ◽  
Numerical Tests ◽  
Shallow Water Models ◽  
Water Models

Finite-Volume Solvers for a Multilayer Saint-Venant SystemWe consider the numerical investigation of two hyperbolic shallow water models. We focus on the treatment of the hyperbolic part. We first recall some efficient finite volume solvers for the classical Saint-Venant system. Then we study their extensions to a new multilayer Saint-Venant system. Finally, we use a kinetic solver to perform some numerical tests which prove that the 2D multilayer Saint-Venant system is a relevant alternative to 3D hydrostatic Navier-Stokes equations.

Numerical Investigation of the “Poor Man’s Navier–Stokes Equations” with Darcy and Forchheimer Terms

2016 ◽  
Vol 26 (05) ◽  
pp. 1650086
Author(s):  
Tingting Tang ◽  
Zhiyong Li ◽  
J. M. McDonough ◽  
P. D. Hislop
Keyword(s):  
Porous Media ◽  
Numerical Investigation ◽  
Stokes Equations ◽  
Discrete Dynamical System ◽  
Flow In Porous Media ◽  
Phase Portraits ◽  
Navier Stokes ◽  
Flow Through Porous Media ◽  
Navier Stokes Equations ◽  
Flow Through

In this paper, a discrete dynamical system (DDS) is derived from the generalized Navier–Stokes equations for incompressible flow in porous media via a Galerkin procedure. The main difference from the previously studied poor man’s Navier–Stokes equations is the addition of forcing terms accounting for linear and nonlinear drag forces of the medium — Darcy and Forchheimer terms. A detailed numerical investigation focusing on the bifurcation parameters due to these additional terms is provided in the form of regime maps, time series, power spectra, phase portraits and basins of attraction, which indicate system behaviors in agreement with expected physical fluid flow through porous media. As concluded from the previous studies, this DDS can be employed in subgrid-scale models of synthetic-velocity form for large-eddy simulation of turbulent flow through porous media.

Sign in / Sign up

Export Citation Format

Share Document