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On the long-time stability of finite element solutions of the navier-stokes equations in a rotating frame of reference

Mine AKBAŞ
2020 Bitlis Eren Üniversitesi Fen Bilimleri Dergisi  
This paper studies the long-time stability behavior of the Navier-Stokes equations (NSE) in a rotating frame of reference with atime accurate and adaptive finite element method.  ...  The proposed numerical scheme consists of two decoupled steps. In the first step, the Navier-Stokes equations are solved with the standard linearized backward-Euler finite element method (BE-FEM).  ...  Therefore, designing a numerical algorithm possessing stability and accuracy at all times is a big challenge in the field of finite element theory, and the long time stability analysis.  ... 
doi:10.17798/bitlisfen.601653 fatcat:2uefiet6sjcijbfdukbbhr2jqa

Longer time simulation of the unsteady Navier-Stokes equations based on a modified convective formulation [article]

Xu Li, Hongxing Rui
2021 arXiv   pre-print
For the discretization of the convective term in the Navier-Stokes equations (NSEs), the commonly used convective formulation (CONV) does not preserve the energy if the divergence constraint is only weakly  ...  The long time numerical simulations show that the linearized and modified convective formulation has a similar performance with the EMAC formulation and outperforms the usual skew-symmetric formulation  ...  Javier de Frutos, Bosco Garcı́a-Archilla, Volker John, and Julia Novo, Analysis of the grad- div stabilization for the time-dependent Navier-Stokes equations with inf-sup stable finite elements  ... 
arXiv:2112.02330v1 fatcat:ouzt56rcozaura4nnuzuitt5gq

Finite elements for scalar convection-dominated equations and incompressible flow problems: a never ending story?

Volker John, Petr Knobloch, Julia Novo
2018 Computing and Visualization in Science  
Second, a number of, in our opinion, important open problems in these fields are discussed. The exposition concentrates on H 1 -conforming finite elements.  ...  First, important recent results concerning finite element methods for convection-dominated problems and incompressible flow problems are described that illustrate the activities in these topics.  ...  The work of P. Knobloch was supported through the grant No. 16-03230S of the Czech Science Foundation. The work of J.  ... 
doi:10.1007/s00791-018-0290-5 fatcat:bohmr5jownfjha5strvss7ivvu

Collision in a cross-shaped domain – A steady 2d Navier–Stokes example demonstrating the importance of mass conservation in CFD

Alexander Linke
2009 Computer Methods in Applied Mechanics and Engineering  
At least, when using conforming Galerkin mixed finite element methods like the Taylor-Hood element, the classical grad-div stabilization for enhancing discrete mass conservation is often neglected in practical  ...  In the numerical simulation of the incompressible Navier-Stokes equations different numerical instabilities can occur.  ...  Below we will present a two-dimensional Navier-Stokes problem with f ≡ 0, demonstrating the importance of mass conservation in numerical approximations of the Navier-Stokes equation.  ... 
doi:10.1016/j.cma.2009.06.016 fatcat:de5motvluzcoronsky23gneg34

A mass, energy, enstrophy and vorticity conserving (MEEVC) mimetic spectral element discretization for the 2D incompressible Navier–Stokes equations

A. Palha, M. Gerritsma
2017 Journal of Computational Physics  
In this work we present a mimetic spectral element discretization for the 2D incompressible Navier-Stokes equations that in the limit of vanishing dissipation exactly preserves mass, kinetic energy, enstrophy  ...  velocity field, and (iii) a conserving time integrator.  ...  Although most of the literature on the simulation of incompressible Navier-Stokes flows has been performed using finite difference and finite volume methods, finite element methods have also been actively  ... 
doi:10.1016/j.jcp.2016.10.009 fatcat:tjlsl3ptmfeordonqqdzys4xau

On Mass‐Conserving Least‐Squares Methods

J. J. Heys, E. Lee, T. A. Manteuffel, S. F. Mccormick
2006 SIAM Journal on Scientific Computing  
A new first-order system reformulation of the Navier-Stokes equations is presented that admits a wider range of mass-conserving boundary conditions.  ...  For the stationary Navier-Stokes equations, which are typically rewritten as a larger system of first-order equations, the loss of mass in the approximate solution is strongly dependent upon the boundary  ...  All of the simulations presented in the results section utilized a trilinear finite element basis for all of the variables unless otherwise noted.  ... 
doi:10.1137/050640928 fatcat:exme7aixozaknj3jid66nb4v2m

A projection-based, semi-implicit time-stepping approach for the Cahn-Hilliard Navier-Stokes equations on adaptive octree meshes [article]

Makrand A. Khanwale, Kumar Saurabh, Masado Ishii, Hari Sundar, James A. Rossmanith, Baskar-Ganapathysubramanian
2021 arXiv   pre-print
We use a projection-based semi-implicit time discretization for the Navier-Stokes and a fully-implicit time discretization for the Cahn-Hilliard equation.  ...  We use a conforming continuous Galerkin (cG) finite element method in space equipped with a residual-based variational multiscale (RBVMS) formulation.  ...  Note the excellent mass conservation across ∼ 260, 000 time steps.  ... 
arXiv:2107.05123v1 fatcat:3clzf6i2jngqta7t5ueoyuuyea

Discrete spectrum analyses for various mixed discretizations of the Stokes eigenproblem

John A. Evans, Thomas J. R. Hughes
2012 Computational Mechanics  
Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining  ...  the data needed, and completing and reviewing the collection of information.  ...  Acknowledgements John A. Evans and Thomas J.R. Hughes were partially supported by the Office of Naval Research under contract number N00014-08-0992. John A.  ... 
doi:10.1007/s00466-012-0788-5 fatcat:b5wvqnqukzbt3g5lsxkdxjs6uu

Euler-Lagrange coupling for porous parachute canopy analysis

Nicolas Aquelet, Benjamin Tutt
2007 International Journal of Multiphysics  
In order to take account of the effect of the parachute permeability, this coupling computes interaction forces based on the Ergun porous flow model.  ...  The method presented couples an Arbitrary Lagrange Euler formulation for the fluid dynamics and an updated Lagrangian finite element formulation for the parachute canopy.  ...  using a Navier-Stokes based Eulerian formulation. • Perform the analyses using conditions similar to a wind tunnel, i.e. infinite mass flow; equating the results to the quasi-steady-descent phase of the  ... 
doi:10.1260/175095407780130517 fatcat:tfcdjvaoabhqvesbq3uzobpex4

A multi-scale method for dynamics simulation in continuum solvent models. I: Finite-difference algorithm for Navier–Stokes equation

Li Xiao, Qin Cai, Zhilin Li, Hongkai Zhao, Ray Luo
2014 Chemical Physics Letters  
This article reports our initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes  ...  A multi-scale framework is proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment  ...  The error in the equilibrium volume is about ~2% when comparing with the analytical value based on mass conservation.  ... 
doi:10.1016/j.cplett.2014.10.033 pmid:25404761 pmcid:PMC4231827 fatcat:y4os5osrlffebnmamy7bjq544i

An adaptive Fixed-Mesh ALE method for free surface flows

Joan Baiges, Ramon Codina, Arnau Pont, Ernesto Castillo
2017 Computer Methods in Applied Mechanics and Engineering  
In this work we present a Fixed-Mesh ALE method for the numerical simulation of free surface flows capable of using an adaptive finite element mesh covering a background domain.  ...  , stabilizing the lack of compatibility between velocity and pressure interpolation spaces, and stabilizing the ill-conditioning introduced by the cuts on the background finite element mesh, and the coupling  ...  Acknowledgements The authors would like to acknowledge Eric Burman for the fruitful discussions on the Ghost Penalty method. This work is partially funded through the ELASTIC-  ... 
doi:10.1016/j.cma.2016.09.041 fatcat:ek7gcckyy5fy5ozpts7drssnze

Slope limiting the velocity field in a discontinuous Galerkin divergence-free two-phase flow solver

Tormod Landet, Kent-Andre Mardal, Mikael Mortensen
2019 Computers & Fluids  
This thesis shows how slope limiting can be used to stabilise the momentum equation in an exactly mass conserving discontinuous Galerkin finite element discretisation of the Navier-Stokes equation.  ...  This thesis describes a finite element method for simulation of free-surface flows, such as ocean waves, using the discontinuous Galerkin method.  ...  "An interior penalty finite element method with discontinuous elements". SIAM journal on numerical analysis 19.4, pp. 742-760. Baker, G. A., Jureidini, W. N., and Karakashian, O. A. (Dec. 1990).  ... 
doi:10.1016/j.compfluid.2019.104322 fatcat:b7ggj2clvjethksh7k5yddc2wq

Page 4455 of Mathematical Reviews Vol. , Issue 2002F [page]

2002 Mathematical Reviews  
The proof uses the fact that the scheme presented is very close to the solution of a stabilized finite element scheme with pressure jump terms across the finite element edges.  ...  In this paper, a covolume scheme for a stabilized mixed method using the simplest approximation spaces Q)-Po for velocity and pressure is applied to the Stokes problem.  ... 

A new fluid structure coupling

Nicolas Aquelet, Benjamin Tutt
2007 European Journal of Computational Mechanics  
In this paper, a new porosity Euler-Lagrange coupling models the fabric permeability by assessing the interaction forces based on the Ergun porous flow model.  ...  an updated Lagrangian finite element formulation for the canopy dynamics.  ...  In Equation 12 , the time t is a fictitious time: in this paper, time step is not updated when solving for the transport equation. There are different ways of splitting the Navier-Stokes problems.  ... 
doi:10.13052/remn.16.521-536 fatcat:e7cyt5mrnbbapnfodo4tsivxlm

High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids

Michael Dumbser, Ilya Peshkov, Evgeniy Romenski, Olindo Zanotti
2016 Journal of Computational Physics  
We apply the successful family of one-step ADER-WENO finite volume and ADER discontinuous Galerkin finite element schemes in the stiff relaxation limit, and compare the numerical results with exact or  ...  A very important key feature of the model is its ability to describe at the same time the behavior of inviscid and viscous compressible Newtonian and non-Newtonian fluids with heat conduction, as well  ...  Last but not least, we would like to thank the two anonymous referees for their constructive comments that helped to improve the clarity and the quality of this paper.  ... 
doi:10.1016/j.jcp.2016.02.015 fatcat:f7mjfzdvsnhcxpoddyu45oywku
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