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A note on the accuracy of the generalized-α scheme for the incompressible Navier-Stokes equations [article]

Ju Liu and Ingrid S. Lan and Oguz Z. Tikenogullari and Alison L. Marsden
2020 arXiv   pre-print
We investigate the temporal accuracy of two generalized-α schemes for the incompressible Navier-Stokes equations.  ...  The conventional approach treats the pressure with the backward Euler method while discretizing the remainder of the Navier-Stokes equations with the generalized-α method.  ...  Acknowledgements This work is supported by the NIH under the award numbers 1R01HL121754, 1R01HL123689, R01EB01830204, the computational resources from the Stanford Research Computing Center, and the Extreme  ... 
arXiv:2002.01098v2 fatcat:qoxojgf3onh4deoqn64ewtvrum

On the accuracy of stiff-accurate diagonal implicit Runge-Kutta methods for finite volume based Navier-Stokes equations [article]

Jiawei Wan, Ahsan Kareem, Haili Liao, Yunzhu Cai
2019 arXiv   pre-print
of the incompressible Navier-Stokes equations on a static collocated grid.  ...  We then propose a new method of applying implicit Runge-Kutta schemes to the time-marching of the index 2 system of the incompressible Navier-Stokes equations.  ...  Acknowledgement The authors gratefully acknowledge the support provided in part by the NSF Grant No. 1562244 and No. 1612843. References  ... 
arXiv:1906.03993v2 fatcat:gs2xmywmdzgphfxenlqppo3gga

Accuracy of Discrete-Velocity BGK Models for the Simulation of the Incompressible Navier-Stokes Equations [article]

Marc B. Reider, James D. Sterling (Center for Nonlinear Studies, Los Alamos National Laboratory)
1993 arXiv   pre-print
We introduce a fourth-order scheme and compare results with those of the commonly used lattice Boltzmann discretization and with finite-difference schemes applied to the incompressible Navier-Stokes equations  ...  A Chapman-Enskog expansion of the PDE system predicts that the macroscopic behavior corresponds to the incompressible Navier-Stokes equations with additional terms of order Mach number squared.  ...  Zou for helpful suggestions. The work was supported by the U.S. Department of Energy at Los Alamos National Laboratory. J.D.S. thanks G. Doolen, J.  ... 
arXiv:comp-gas/9307003v1 fatcat:qjbldykma5avvnqnffgdbxd2mi

A posteriori error estimation for the fractional step theta discretization of the incompressible Navier–Stokes equations

Dominik Meidner, Thomas Richter
2015 Computer Methods in Applied Mechanics and Engineering  
As time discretization scheme we consider the fractional step theta method, that consists of three subsequent steps of the one-step theta method.  ...  The derived error estimator is based on a mathematical trick: we define an intermediate time-discretization scheme based on a Petrov-Galerkin formulation.  ...  The focus of Section 2 will be a Galerkin formulation for the incompressible Navier-Stokes equations similar to the theta method.  ... 
doi:10.1016/j.cma.2014.11.031 fatcat:yi3zkje7qbbq3biw4524swenai

Numerical simulations of unsteady viscous incompressible flows using general pressure equation

Adrien Toutant
2018 Journal of Computational Physics  
The proposed general pressure equation (GPE) allows to solve general, time-accurate , incompressible Navier-Stokes flows.  ...  It consists in using a general pressure equation (GPE) derived from compressible Navier-Stokes equation.  ...  Computational approach The classical incompressible Navier-Stokes (INS) equations consist of the equation for the momentum and the continuity equation: ∂ t u α + ∂ β (u β u α ) + ∂ α P = 1 Re ∂ β ∂ β u  ... 
doi:10.1016/j.jcp.2018.07.058 fatcat:idtssmhflnb4zo2drkp5vp3qde

High-order flux reconstruction method for the hyperbolic formulation of the incompressible Navier-Stokes equations on unstructured grids [article]

Mohamed M. Kamra, Jabir Al-Salami, Changhong Hu
2021 arXiv   pre-print
A high-order Flux reconstruction implementation of the hyperbolic formulation for the incompressible Navier-Stokes equation is presented.  ...  Instead of splitting the second-order conservation law into two equations, one for the solution and another for the gradient, the Navier-Stokes equation is cast into a first-order hyperbolic system of  ...  The numerical calculations were carried out on the TSUBAME 3.0 supercomputer at Tokyo Institute of Technology.  ... 
arXiv:2106.01579v1 fatcat:sezxyilkmrfxpllxymzi5klloy

A new family of projection schemes for the incompressible Navier–Stokes equations with control of high-frequency damping

A. Lovrić, Wulf G. Dettmer, Chennakesava Kadapa, Djordje Perić
2018 Computer Methods in Applied Mechanics and Engineering  
A new family of projection schemes for the incompressible Navier-Stokes equations with control of high-frequency damping.  ...  This choice does not imply a loss of generality, but allows for a clearer presentation which is more aligned with the formulation for the incompressible Navier-Stokes equations in Section 3.  ...  In Section 3, the projection methods are formulated for the incompressible Navier-Stokes equations using finite elements.  ... 
doi:10.1016/j.cma.2018.05.006 fatcat:oj45uimzljd4fiy6np2wefiane

Fourth order compact schemes for variable coefficient parabolic problems with mixed derivatives [article]

Shuvam Sen
2013 arXiv   pre-print
The fact that the method has been particularly developed for parabolic equations with mixed derivatives makes it suitable for solving incompressible Navier-Stokes (N-S) equations in irregular domains.  ...  The finite difference scheme, presented here for two-dimensional domains, is based on fourth order spatial discretization.  ...  In the first part, we present the HOC difference scheme for Eq. (1) and its extension to the 2D incompressible Navier-Stokes equations.  ... 
arXiv:1312.5112v1 fatcat:f7mb7nfpzjb2dfynvhc46podfq

The Splitting Algorithm in Finite Volume Method for Numericai Solving of Navier-Stokes Equations of Viscous Incompressible Fluids

Viktor M. Kovenya, Novosibirsk State University, Daniel Tarraf
2001 Journal of Siberian Federal University Mathematics & Physics  
For the numerical solution of the Navier-Stokes equations, written in an integral form, an implicit of finite-volume algorithm is proposed, which is a generalization of previously proposed differences  ...  The numerical test of the algorithm on the exact solution, in problems about the viscosity flow in the cavern with a moving lid and the current of the heated walls of the channel, confirmed the sufficient  ...  Conclusion The paper proposes a generalization of the finite difference splitting scheme for the numerical solution of the Navier-Stokes equations of a viscous incompressible fluid to the finite volume  ... 
doi:10.17516/1997-1397-2021-14-4-519-527 fatcat:2panblbzvvg7fov4hzfmgmcnou

Temporal Integrators for Fluctuating Hydrodynamics [article]

S. Delong and B. E. Griffith and E. Vanden-Eijnden and A. Donev
2012 arXiv   pre-print
We describe finite-volume spatial discretizations for the fluctuating Burgers and fluctuating incompressible Navier-Stokes equations that obey a discrete fluctuation-dissipation balance principle just  ...  Numerical results demonstrate that a midpoint predictor-corrector scheme is very robust over a broad range of time step sizes.  ...  Acknowledgments We would like to thank John Bell, Alejandro Garcia, and Jonathan Goodman for numerous enlightening discussions.  ... 
arXiv:1212.1033v2 fatcat:5u3bli6qpzbyth7apd65bmpvz4

High-order arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for the incompressible Navier-Stokes equations [article]

Niklas Fehn, Johannes Heinz, Wolfgang A. Wall, Martin Kronbichler
2020 arXiv   pre-print
This paper presents robust discontinuous Galerkin methods for the incompressible Navier-Stokes equations on moving meshes.  ...  The Navier-Stokes equations with ALE transport term are solved on the deformed geometry storing one instance of the mesh that is updated from one time step to the next.  ...  Acknowledgments The research presented in this paper was partly funded by the German Research Foundation (DFG) under the project "High-order discontinuous Galerkin for the exa-scale" (ExaDG) within the  ... 
arXiv:2003.07166v1 fatcat:g6etpk32lfh4tn33chppcnjk2q

Normal mode analysis of second-order projection methods for incompressible flows

Jie Shen, Jae-Hong Pyo
2005 Discrete and continuous dynamical systems. Series B  
It is shown that although the two schemes provide second-order accuracy for the velocity in L 2 -norm, their accuracies for the velocity in H 1 -norm and for the pressure in L 2norm are different, and  ...  only the Gauge-Uzawa scheme introduced provides full second-order accuracy for all variable in their natural norms.  ...  So the general normal mode solution of Navier-Stokes equations is (u, p)(x, y, t) = k s α k,s exp(σ k,Is · t)(ū k,Is ,p k,Is )(x) exp(ky) where α k,s and β k,s are constants in the given initial velocity  ... 
doi:10.3934/dcdsb.2005.5.817 fatcat:mhaef4rxk5hglm72lgeo74m3qq

A fully semi-Lagrangian discretization for the 2D incompressible Navier–Stokes equations in the vorticity-streamfunction formulation

Luca Bonaventura, Roberto Ferretti, Lorenzo Rocchi
2018 Applied Mathematics and Computation  
A numerical method for the two-dimensional, incompressible Navier--Stokes equations in vorticity--streamfunction form is proposed, which employs semi-Lagrangian discretizations for both the advection and  ...  Numerical experiments on classical benchmarks for incompressible flow in simple geometries validate the proposed method.  ...  Acknowledgements Part of this research work has been financially supported by the INDAM-GNCS project "Metodi numerici semi-impliciti e semi-Lagrangiani per sistemi iperbolici di leggi di bilancio" and  ... 
doi:10.1016/j.amc.2017.11.030 fatcat:ofeqzbxghndrlcrorewtmgilta

Moving Mesh Finite Element Methods for the Incompressible Navier--Stokes Equations

Yana Di, Ruo Li, Tao Tang, Pingwen Zhang
2005 SIAM Journal on Scientific Computing  
This work presents the first effort in designing a moving mesh algorithm to solve the incompressible Navier-Stokes equations in the primitive variables formulation.  ...  Selecting suitable monitor functions is important and is found challenging for the incompressible flow simulations, which is the second goal of this study.  ...  We thank the referees for useful comments and suggestions. The major portion of this research was carried out while the first author was visiting the Hong Kong Baptist University.  ... 
doi:10.1137/030600643 fatcat:vcvaqkjmdjcyhhfotwuiebkhoy

On the Numerical Solution of the Incompressible Navier-Stokes Equations in Primitive Variables Using Grid Generation Techniques

S. A. Salem
2006 Mathematical and Computational Applications  
In this paper presents a new model procedure for the solution of the incompressible Navier-Stokes equations in primitive variables, using grid generation techniques.  ...  Results obtained for the model problem of driven flow in a square cavity demonstrate that the method yields accurate solutions.  ...  INTRODUCTION We shall describe a combination of numerical grid generation techniques using stretching function by Marcel Vinkur [9] for solving the incompressible Navier-Stokes equations in primitive  ... 
doi:10.3390/mca11020127 fatcat:qfwatisyljat7oxletijzkzn4i
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