Systematic Comparison of Finite-Volume Calculation Methods With Staggered and Nonstaggered Grid Arrangements

Choi, Seok-Ki; Nam, Hyun-Yeol; Cho, Mann

doi:10.1080/10407799408955918

Cited by 28 publications

(15 citation statements)

References 10 publications

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“…Collocated meshes are known to generate spatially oscillating, checkerboard-like pressure fields, which can be eliminated through the so-called momentum interpolation, due to Rhie and Chow [23], by which continuity is no longer satisfied in its discretized form, but only in the limit of refinement, according to the order of the scheme. Despite the oscillating pressure field or, alternatively, the nonconservation of mass in the discrete sense, studies [4,[24][25][26][27] indicate that the accuracy of the velocity field, the stability, and the convergence characteristics of the cell-center collocated meshes are comparable to those of the staggered mesh.…”

Section: Introductionmentioning

confidence: 91%

Comparative Study of the Accuracy of the Fundamental Mesh Structures for the Numerical Solution of Incompressible Navier-Stokes Equations in the Two-Dimensional Cavity Problem

Figueiredo

Oliveira

2009

Numerical Heat Transfer, Part B: Fundamentals

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The accuracies of the staggered, semistaggered, vertex collocated, and cell-center collocated meshes are compared for the incompressible Navier-Stokes equations in primitive variables using the two-dimensional lid-driven cavity test problem in both the traditional form with uniform lid velocity and in the regularized form without corner discontinuities. Central differencing is used in all discretizations. The momentum equations are integrated explicitly after the solution of a Poisson pressure equation that enforces mass conservation. Richardson extrapolation is employed to estimate the correct solutions in cases without precise reference solutions. For both forms of the problem, the staggered and the cell-center collocated meshes are shown to produce comparably accurate results, while the vertex collocated mesh shows poorer accuracy. The almost unknown semistaggered mesh, which is too sensitive to the velocity discontinuity in the traditional cavity problem, appears as the most accurate mesh in the regularized cavity problem.

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Section: Introductionmentioning

confidence: 91%

Comparative Study of the Accuracy of the Fundamental Mesh Structures for the Numerical Solution of Incompressible Navier-Stokes Equations in the Two-Dimensional Cavity Problem

Figueiredo

Oliveira

2009

Numerical Heat Transfer, Part B: Fundamentals

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“…A similar expression can be obtained for the north face velocity 6 n =Q n (6)+6 n −Q n (6 ). (20) The proposed interpolation is more appropriate when used in combination with the QUICK differencing scheme, where the convected cell-face velocities are approximated to third-order by formulae (16) and (17), setting =u or 6. The Rhie and Chow momentum interpolation of the convecting cell-face velocities is of only second-order (the order of linear interpolation, see Miller and Schmidt [11]).…”

Section: Quadratic Momentum Interpolationmentioning

confidence: 99%

“…These values are needed for the evaluation of the correction part of cell-face velocities according to the above interpolation practice, and also for the calculation of the pressure gradient source term in the momentum equations. The interpolation equations used are (16) and (17), where = P.…”

Section: E6aluation Of Cell-face Pressuresmentioning

confidence: 99%

Enhancement of the momentum interpolation method on non-staggered grids

Papageorgakopoulos

Arampatzis

Assimacopoulos

et al. 2000

Int. J. Numer. Meth. Fluids

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A novel interpretation of the momentum interpolation method (MIM) is presented in this paper. A revised method using quadratic interpolating polynomials for the calculation of the cell-face velocities is proposed. The performance of the proposed method (referred to as QMIM) is examined and its application to the well-known lid-driven flow in a square enclosure problem is tested. The computed results are compared with standard reported benchmark solutions for a wide range of flow conditions. The numerical experiments show clearly the superiority of the new approach over the original MIM, in terms of numerical accuracy, rate of convergence towards the grid-independent solution, and computational efficiency.

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“…The symmetry and uniform distribution of the grid is suppose to amplify any problems that may be associated with the non-staggered methodology. For example, this problem and the similar problem of buoyancy-driven recirculation in a square cavity has been studied in a number of papers which test a non-staggered methodology, refer to, for example, References [25,26,32,45,46]. In this investigation various grid systems are employed consisting of 20× 20, 40× 40, 60×60 and 100×100 grid points.…”

Section: Laminar Flow In a Square Ca6ity With A Dri6en Lidmentioning

confidence: 99%

Finite difference scheme for the solution of fluid flow problems on non‐staggered grids

Barton

Kirby

2000

Numerical Methods in Fluids

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Systematic Comparison of Finite-Volume Calculation Methods With Staggered and Nonstaggered Grid Arrangements

Cited by 28 publications

References 10 publications

Comparative Study of the Accuracy of the Fundamental Mesh Structures for the Numerical Solution of Incompressible Navier-Stokes Equations in the Two-Dimensional Cavity Problem

Comparative Study of the Accuracy of the Fundamental Mesh Structures for the Numerical Solution of Incompressible Navier-Stokes Equations in the Two-Dimensional Cavity Problem

Enhancement of the momentum interpolation method on non-staggered grids

Finite difference scheme for the solution of fluid flow problems on non‐staggered grids

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