This is a scientific web page about the two-dimensional steady incompressible flow in a driven cavity. The steady incompressible 2-D Navier-Stokes equations are solved numerically. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. This is a scientific web page about the two-dimensional steady incompressible flow in a driven cavity. The steady incompressible 2-D Navier-Stokes equations are solved numerically. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations.

LID DRIVEN CAVITY FLOW

In this web page you will find my research on Steady Incompressible 2-D Flows such as Driven Cavity Flow or Flow Over a Backwards Facing Step. I discuss about physical, mathematical and numerical aspects of these flows, post many figures and tables, also post fortran codes, solution datas and etc.

     In this study Erturk et. al. presented a new, efficient and stable numerical method for 2-D Steady Incompressible Navier-Stokes equations in streamfunction and vorticity formulation. Using this numerical method Erturk et. al. solved the driven cavity flow up to Reynolds number of 21,000. I post all of my numerical solution data presented in the manuscript and also the fortran solver used in this study available for download.

  • Erturk E, Corke TC and Gokcol C, "Numerical Solutions of 2-D Steady Incompressible Driven Cavity Flow at High Reynolds Numbers", International Journal for Numerical Methods in Fluids 2005, Vol 48, pp 747-774

     In this study Erturk E. discussed the 2-D Steady Incompressible flow in the driven cavity in terms of mathematical, physical and numerical aspects with a perspective to answer "is the flow in driven cavity stable or not", or "should it be stable or not". E. Erturk also presented very very fine grid solutions of driven cavity flow simply solved with using Successive Over Relaxation Method (SOR). I post all of my numerical solution data presented in the manuscript and also the fortran solver used in this study available for download.

  • Erturk E, "Discussions on Driven Cavity Flow", International Journal for Numerical Methods in Fluids 2009, Vol 60, pp 275-294

     In this study Erturk E. and Gokcol C. presented a new and very efficient HOC (High Order Compact) formulation for 2-D Steady Incompressible Navier-Stokes equations. Using this formulation, any existing solver that solves the 2-D Steady Incompressible Navier-Stokes equations with second order spatial accuracy can be easily modified to provide fourth order spatial accuracy. With this formulation they solved the flow in a driven cavity up to Reynolds number of 20,000 with fourth order spatial accuracy using very fine grid mesh. I post all of my numerical solution data presented in the manuscript and also the fortran solver used in this study available for download.

  • Erturk E and Gokcol C, "Fourth Order Compact Formulation of Navier-Stokes Equations and Driven Cavity Flow at High Reynolds Numbers", International Journal for Numerical Methods in Fluids 2006, Vol 50, pp 421-436

     In this study Erturk E. and Gokcol O. solved the 2-D steady incompressible flow inside a triangular driven cavity and obtained highly accurate solutions using a fine grid mesh. Detailed solutions of flow inside various tringle cavity geometries are presented. I post all of my numerical solution data presented in the manuscript and also the fortran solver used in this study available for download.

  • Erturk E and Gokcol O, "Fine Grid Numerical Solutions of Triangular Cavity Flow", The European Physical Journal - Applied Physics 2007, Vol 38, pp 97-105

     In this study Erturk E. reintroduced the benchmark problem "driven skewed cavity flow", originally introduced by Demirdzic et al., with a variety of skew angles and then applied the numerical method presented in "Study 1" to 2-D steady incompressible flow in a skewed cavity. The numerical method proved to be very efficient for the solution of N-S Equations in general curvilinear coordinates in non-orthogonal geometries even at extreme skew angles. Detailed solutions are presented for future references. I post all of my numerical solution data presented in the manuscript available for download.

  • Erturk E and Dursun B, "Numerical Solutions of 2-D Steady Incompressible Flow in a Driven Skewed Cavity", ZAMM - Journal of Applied Mathematics and Mechanics 2007, Vol 87, pp 377-392

     In this study Erturk E. presented numerical solutions of 2-D steady incompressible flow over a backward facing step. Using the efficient and stable numerical method described above in "Study 1" the backward facing step flow is solved for high Reynolds numbers. Detailed results are presented.

  • Erturk E, "Numerical Solutions of 2-D Steady Incompressible Flow Over a Backward-Facing Step, Part I: High Reynolds Number Solutions", Computers & Fluids 2008, Vol 37, pp 633-655

     In this study Erturk E. presented the numerical performance of the fourth order compact O (Dx4) formulation of the steady 2-D incompressible Navier-Stokes equations introduced by Erturk et al. (Int. J. Numer. Methods Fluids, 50, 421-436).

  • Erturk E, "Numerical Performance of Compact Fourth Order Formulation of the Navier-Stokes Equations", Communications in Numerical Methods in Engineering 2008, Vol 24, pp 2003-2019

     In finite difference, one can obtain fourth order O (Dx4) accurate numerical solutions using the compact formulation. One can also obtain fourth order accurate O (Dx4) numerical solutions using the standart five point wide discretization. In this study Erturk E. compared the numerical performance of the fourth order compact and fourth order wide formulations of the steady 2-D incompressible Navier-Stokes equations.

  • Erturk E, "Comparison of Wide and Compact Fourth Order Formulations of the Navier-Stokes Equations", International Journal for Numerical Methods in Fluids 2009, Vol 60, pp 992-1010

     In this study, the fourth order compact formulation introduced by Erturk and Gokcol (Int. J. Numer. Methods Fluids, 50, 421-436) is extended to non-uniform grids. The advantage of this formulation is that the presented formulation provides fourth order O (Dx4) spatial accuracy on non-uniform grids. The efficiency of the formulation is demonstrated on the lid driven cavity flow benchmark problem.

  • Erturk E and Gokcol O, "Fourth Order Compact Formulation of Steady Navier-Stokes Equations on Non-Uniform Grids", International Journal of Mechanical Engineering and Technology 2018, Vol 9, pp 1379-1389

     In this study Erturk E. presented benchmark numerical solutions of 2-D steady incompressible flow in a driven polar cavity at high Reynolds numbers. The polar cavity is considered as both driven from inside wall and from outside wall. Using a fine grid mesh with 513×513 points, the steady driven polar cavity flow is solved for Re17500. The computed results are compared with experimental and numerical results. Detailed numerical results of the driven polar cavity flow are presented. I post all of my numerical solution data presented in the manuscript available for download.

  • Erturk E, "Benchmark Solutions of Driven Polar Cavity Flow at High Reynolds Numbers", International Journal of Mechanical Engineering and Technology 2018, Vol 9, pp 776-786

     In this study Erturk E. and Gokcol O. solved the 2-D steady incompressible flow around a circular cylinder at high Reynolds numbers. Using a very efficient numerical method and a very large mesh, numerical solutions are obtained up to Reynolds number of 500. It is found that the solution of 2-D steady incompressible flow around a circular cylinder change behavior around Reynolds number of 100 and 300. Detailed numerical results of the flow over a circular cylinder are presented. I post all of my numerical solution data presented in the manuscript available for download.

  • Erturk E and Gokcol O, "Numerical Solutions of Steady Incompressible Flow Around a Circular Cylinder Up To Reynolds Number 500", International Journal of Mechanical Engineering and Technology 2018, Vol 9, pp 1368-1378

     In this study Erturk E. and Gokcol O. presented numerical simulations of the steady incompressible viscous flow over a square cylinder. Using an efficient finite difference numerical method together with a very large mesh, highly accurate steady solutions are obtained up to Reynolds number of 200. Our numerical results indicate that the strength of the vorticity at the center of the separation bubble increases until Re=100 and then starts to decrease with increasing Reynolds number. Detailed numerical solutions are presented. I post all of my numerical solution data presented in the manuscript available for download.

  • Erturk E and Gokcol O, "Steady Flow over a Square Cylinder at High Reynolds Numbers", International Journal of Mechanical Engineering and Technology 2018, Vol 9, pp 638-649

     In this study Erturk E. and Gokcol O. numerically simulated the steady incompressible viscous flow past a square cylinder confined in a channel. The considered channel has a blockage ratio of 1/8. The governing 2-D steady incompressible Navier-Stokes equations are solved with a very efficient finite difference numerical method using a very large stretched mesh such that the inflow and the outflow boundary is located very far away from the square cylinder. The numerical solutions of steady incompressible viscous flow around a square cylinder confined in a channel with 1/8 blockage ratio is obtained up to Reynolds number of 410. Detailed results of the flow characteristics are presented. I post all of my numerical solution data presented in the manuscript available for download.

  • Erturk E and Gokcol O, "High Reynolds Number Solutions of Steady Incompressible 2-D Flow around a Square Cylinder Confined in a Channel with 1/8 Blockage Ratio", International Journal of Mechanical Engineering and Technology 2018, Vol 9, pp 452-463

     In this study Erturk E. and Gokcol O. numerically investigated the effect of the blockage ratio on the steady incompressible viscous flow past a square cylinder confined in a channel. In terms of the channel height with respect to the length of the square cylinder 1/4, 1/6, 1/8 and 1/10 blockage ratios are considered. For each of the considered blockage ratio the flow past a square cylinder confined in a channel is simulated up to very high Reynolds numbers. The numerical solutions of different channel blockage ratios are compared with each other and detailed results are presented.

  • Erturk E and Gokcol O, "Effect of Blockage Ratio on Steady Incompressible 2-D Flow around a Square Cylinder Confined in a Channel", International Journal of Mechanical Engineering and Technology 2018, Vol 9, pp 477-487

     In this study Erturk E. and Gokcol O. presented a fourth order compact scheme for the streamfunction-vorticity formulation of the steady incompressible Navier-Stokes equations in polar coordinates. The solutions of the presented compact streamfunction and vorticity formulations are spatially forth order accurate. These compact formulations provide high spatial accuracy even with using coarser grid points in the computational domain. The efficiency of the formulation is demonstrated on the driven polar cavity flow benchmark problem.

  • Erturk E and Gokcol O, "Fourth Order Compact Scheme for Streamfunction-Vorticity Formulation of the Navier-Stokes Equations in Polar Coordinates", International Journal of Mechanical Engineering and Technology 2018, Vol 9, pp 1327-1336

     In this study Erturk E. and Gokcol O. numerically investigated the effect of the incidence angle on the steady incompressible viscous flow past a square cylinder confined in a channel. A blockage ratio of 1/6 which is defined as the ratio of the frontal area to the channel height is considered. The square cylinder is considered to have both 0 and 45 incidence angles to the incoming flow. The steady incompressible solutions are obtained for high Reynolds numbers. The solutions of the square cylinder with 45 incidence angle is compared with 0 incidence angle square cylinder in order to demonstrate the effect of the incidence angle on the flow problem. Detailed results are presented.

  • Erturk E and Gokcol O, "Flow Past a Square Cylinder Confined in a Channel with Incidence Angle", International Journal of Mechanical Engineering and Technology 2018, Vol 9, pp 1642-1652

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