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Local Method of Approximate Particular Solutions for Two-Dimensional Unsteady Incompressible Flow

Juraj Muzik, Ladislav Kais, Roman Bulko
2016 Communications - Scientific Letters of the University of Zilina  
The method solves the incompressible Navier-Stokes equations in terms of theprimitive variables using the fractional step scheme.  ...  A meshless local method of approximated particular solutions (LMAPS) is used to analyze incompressible fluid flow in a two dimensionalcavity.  ...  Lid-driven cavity flow is used as a standard test problem for the validation of numerical solutions of incompressible Navier-Stokes flow.  ... 
doi:10.26552/com.c.2016.4.77-82 fatcat:scy2u54tvnhjngxsiw6vy5jfpi

Contents [chapter]

2022 Numerical Simulation of Incompressible Viscous Flow  
for the generalized Stokes 8 problems | 60 Further applications (II): On the simulation of the lid-driven cavity flow of an 4.7 Appendix C: Conjugate gradient methods for the solution of Oldroyd-B fluid  ...  /fictitious-domain method for simulating lid-driven viscous flows in a hemispherical 3 Advection problems | 23 cavity | 144 3.1 7.1 The wave-like equation method | 23 Introduction to fictitious-domain  ... 
doi:10.1515/9783110785012-toc fatcat:62b4gpmwarerfemzola4ojc5ou

The Boundary Knot Method for Simulating Unsteady Incompressible Fluid Flow

Juraj Mužík
2015 Procedia Engineering  
This article presents a numerical algorithm using the Boundary knot (BK) method for the incompressible Navier-Stokes equations.  ...  In numerical examples the reverse principle with thin plate spline (TPS) radial basis functions (RBF) is used to construct the particular solution.  ...  Acknowledgements This contribution is the result of the project "Research centre of the University of Žilina" (ITMS 26220220183) supported by the Research and Development Operational Programme funded by  ... 
doi:10.1016/j.proeng.2015.07.046 fatcat:6fqpqxbz6fgfxlx4eqb6lcdr2u

A Comparison between the Reduced Differential Transform Method and Perturbation-Iteration Algorithm for Solving Two-Dimensional Unsteady Incompressible Navier-Stokes Equations

Abdul-Sattar J. Al-Saif, Assma J. Harfash
2018 Journal of Applied Mathematics and Physics  
In this work, approximate analytical solutions to the lid-driven square cavity flow problem, which satisfied two-dimensional unsteady incompressible Navier-Stokes equations, are presented using the kinetically  ...  In [7], Chebyshev-collocation method in space is introduced with Adams-Bashforth backward-Euler scheme for the time integration to calculate the solution of three-dimensional lid-driven cavity flows.  ...  Conflicts of Interest The authors declare no conflicts of interest regarding the publication of this paper.  ... 
doi:10.4236/jamp.2018.612211 fatcat:vnbm2tpksbggje2di7boyvjedu

Development of openfoam solvers for incompressible navier–stokes equations based on high-order runge–kutta schemes

V. D'Alessandro, A. Zoppi, L. Binci, R. Ricci
2016 International Journal of Computational Methods & Experimental Measurements  
Therefore in this work we have developed several solvers for incompressible Navier-Stokes equations (NSE) based on high-order explicit and implicit Runge-Kutta (RK) schemes for time-integration.  ...  Moreover several benchmark solutions have been computed in order to assess the reliability, the accuracy and the robustness of the presented solvers.  ...  Lid-driven cavity flow As first test case, we consider the two-dimensional lid-driven cavity flow. The computational domain for this problem is a box with edges of unit length.  ... 
doi:10.2495/cmem-v4-n4-594-603 fatcat:3fosmwec4ffpbeit7v4gtvgeoe

An Exponential Time Integrator for the Incompressible Navier--Stokes Equation

Gijs L. Kooij, Mike A. Botchev, Bernard J. Geurts
2018 SIAM Journal on Scientific Computing  
The new time integration method is tested in several numerical experiments including the Taylor-Green vortex and a lid-driven cavity flow.  ...  The incompressible Navier-Stokes equation, discretized in space, is a differentialalgebraic equation where a time derivative for the pressure is absent.  ...  time-parallel method, measuring the performance benefit as function of problem size and number of processors.  ... 
doi:10.1137/17m1121950 fatcat:g6bjd4htzrg4zlxfh7q45cie4i

A variational multiscale Newton-Schur approach for the incompressible Navier-Stokes equations [article]

D. Z. Turner, K. B. Nakshatrala, K. D. Hjelmstad
2008 arXiv   pre-print
In the following paper, we present a consistent Newton-Schur solution approach for variational multiscale formulations of the time-dependent Navier-Stokes equations in three dimensions.  ...  Using a variational multiscale framework, we construct a two-level approach to stabilizing the incompressible Navier-Stokes equations based on a coarse and fine-scale subproblem.  ...  lid-driven cavity problem for Re = 800 which were obtained by direct solution of the steady state Navier-Stokes equations using the Newton-Schur solution approach.  ... 
arXiv:0809.4802v1 fatcat:nehc62b2qnf7bftlc6uv4nbdda

Smoothed Particles Hydrodynamics – the implementations of the incompressibility

Kamil Szewc
2010 Copernican Letters  
The Smoothed Particle Hydrodynamics (SPH) is a fully Lagrangian, grid-free technique for fluid-flow simulations.  ...  An important and open issue in the SPH is a proper implementation of the incompressibility constraint. Generally there are two ways to deal with this problem.  ...  Lid-driven cavity flow The lid-driven cavity common test of numerical algorithms for viscous flows.  ... 
doi:10.12775/cl.2010.020 fatcat:b4zeq73rmvcjdhhcu4yrpv37oa

A hybrid vertex-centered finite volume/element method for viscous incompressible flows on non-staggered unstructured meshes

Wei Gao, Ru-Xun Liu, Hong Li
2012 Acta Mechanica Sinica  
This paper proposes a hybrid vertex-centered finite volume/finite element method for solution of the two dimensional (2D) incompressible Navier-Stokes equations on unstructured grids.  ...  The classic test cases, the lid-driven cavity flow, the skew cavity flow and the backward-facing step flow, show that numerical results are in good agreement with the published benchmark solutions.  ...  Numerical method The fractional step method is popular for solving incompressible Navier-Stokes equations (1) and (2) in terms of the primitive variables.  ... 
doi:10.1007/s10409-012-0038-2 fatcat:h4mhggbklbbznfi7qjblrheod4

Finite element simulation of three-dimensional particulate flows using mixture models

Yuliya Gorb, Otto Mierka, Liudmila Rivkind, Dmitri Kuzmin
2014 Journal of Computational and Applied Mathematics  
A numerical study of the proposed approach is performed for 3D particulate flows over a backward-facing step and in a lid-driven cavity.  ...  The generalized Navier-Stokes system and the continuity equation for the volume fraction of the disperse phase are discretized using an implicit high-resolution finite element scheme, and maximum principles  ...  Acknowledgments The work of the first author was supported by NSF grant DMS-1016531.  ... 
doi:10.1016/j.cam.2013.12.020 fatcat:rawmnlqwwjfahpybxq2cy2pr54

A Multi-Dimensional Virtual Characteristic Scheme for Laminar and Turbulent Incompressible Flows

Seyed Esmail Razavi, Masoud Hanifi
2016 Journal of Applied Fluid Mechanics  
This scheme is applied to the flows between parallel plates, over backward-facing step, and in square lid-driven cavity at a wide range of Reynolds numbers.  ...  A multi-dimensional virtual characteristic-based scheme (MVCB) by the aid of artificial compressibility is developed for convective fluxes in laminar and turbulent incompressible flows.  ...  NUMERICAL RESULTS The proposed scheme was applied for flow simulations in a channel, over backward-facing step, and for lid-driven cavity in the laminar and turbulent regimes.  ... 
doi:10.18869/acadpub.jafm.68.235.25149 fatcat:dmhv33cjzbgavdp5tmnbjgry7m

Comparison Of Pressure Based Solver With Artificial Compressibility Method

Sachin K.M, Vinay S.S, N. Sreenivasulu Reddy
2014 International Journal of Engineering Research  
In this paper, various interpolation schemes are used to simulate the velocity behaviour of viscous incompressible fluids on standard lid driven cavity test case.  ...  Pressure based solver (PBS) is an algorithm to solve the pressure equation which is derived from the continuity and momentum equations.  ...  Fig. 1 1 Overview of the Pressure-Based Solution Fig. 2 2 Geometry of the lid driven cavity.Incompressible flow in a two-dimensional square domain.  ... 
doi:10.17950/ijer/v3s7/715 fatcat:gnjoyixiq5g3bkpzqnznfecbiu

A Relationship between Stabilized FEM and Bubble Function Element Stabilization Mthod with Orthogonal Basis for Incompressible Flows

Junichi MATSUMOTO
2005 Journal of Applied Mechanics  
stabilization method with orthogonal basis is shown for the unsteady and steady Navier-Stokes equations.  ...  A two-level three-level formulation with bubble function, a bubble function element stabilization method, is proposed for incompressible viscous flow.  ...  element methods for the incompressible Navier-Stokes equations in advection dominated flows, Int.  ... 
doi:10.2208/journalam.8.233 fatcat:5kyb4xf5drap7e6zmmryjl6h4a

A stabilized finite element method for stochastic incompressible Navier–Stokes equations

Mofdi El-Amrani, Mohammed Seaid, Mostafa Zahri
2012 International Journal of Computer Mathematics  
Acknowledgements This work was partly performed while the second author was a visiting professor at the Department of Mathematics, University of Taibah at Madinah. M.  ...  Seaïd is deeply grateful to Taibah University for their hospitality during a research visit there. M.  ...  For instance, we have presented numerical results for an accuracy test problem with analytical solution, for the stochastic lid-driven cavity flow problem and for the stochastic natural convection in a  ... 
doi:10.1080/00207160.2012.696620 fatcat:7k3qhvbt7zhezjpltx5nztgswa

A Unified Fractional-Step, Artificial Compressibility and Pressure-Projection Formulation for Solving the Incompressible Navier-Stokes Equations

László Könözsy, Dimitris Drikakis
2014 Communications in Computational Physics  
AbstractThis paper introduces a unified concept and algorithm for the fractional-step (FS), artificial compressibility (AC) and pressure-projection (PP) methods for solving the incompressible Navier-Stokes  ...  Therefore, the proposed FSAC-PP approach unifies the fully-explicit AC and semi-implicit FS-PP methods of Chorin including a PP step in the dual-time stepping procedure to a) overcome the numerical stiffness  ...  Acknowledgments The authors would like to acknowledge Tommaso Oggian's assistance regarding the implementation of the pressure-Poisson solver.  ... 
doi:10.4208/cicp.240713.080514a fatcat:oefpxzynubed3hshgbhkbm6fku
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