Numerical Solution of Navier-Stokes Equations With Nonstaggered Grids Using Finite Analytic Method

Aksoy, Hakan; Chen, Ching-Jen

doi:10.1080/10407799208944906

Cited by 21 publications

(15 citation statements)

References 10 publications

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“…[5] that reduces the oscillations at the cost of increasing notably the computational burden. Later, a rather close interpolation to PWIM named MWIM was proposed by Aksoy and Chen [6]. The only difference between both approaches lies in the quantity chosen to be interpolated, a complete term interpolation, PWIM, or a factor-in-term interpolation, MWIM.…”

Section: Introductionmentioning

confidence: 99%

“…The reason why PICTURETWO is inconsistent is that its solution in the steady limit does not correspond to the steady solution, unless ρ i ∆V i = ρ e ∆V e in which case is identical to Kadja et al's scheme. We can thus assure that in a general case the PICTURETWO solution will be independent of ∆t but dependent on the cell mass variation 6 because Eq. 61 can always be written as e ∆V e so the equivalence to Kadja et al's approach is obvious.…”

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confidence: 99%

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Cell face velocity alternatives in a structured colocated grid for the unsteady Navier–Stokes equations

Pascau

2011

Numerical Methods in Fluids

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The use of a colocated variable arrangement for the numerical solution of fluid flow is becoming more and more popular due to its coding simplicity. The inherent decoupling of the pressure and velocity fields in this arrangement can be handled via a special interpolation procedure for the calculation of the cell face velocity named PWIM (Pressure Weighted Interpolation Method). In this paper a discussion on the alternatives to extend PWIM to unsteady flows is presented along with a very simple criterium to ascertain if a given interpolation practice will produce steady results that are relaxation dependent or time step dependent. Following this criterium it will be shown that some prior schemes presented as time step independent are actually not, although by using special interpolations can be readily adapted to be. A systematic way of deriving different cell face velocity expressions will be presented and new formulae free of ∆t dependence will be derived. Several computational exercices will accompany the theoretical discussion to support our claims.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

Cell face velocity alternatives in a structured colocated grid for the unsteady Navier–Stokes equations

Pascau

2011

Numerical Methods in Fluids

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“…e u and n v , are substituted directly into the continuity equation (6) (8) to solve the pressure equation are not available. Various available non-staggered grid algorithms proposed (Abdallah 1987, Miller and Schmidt 1988, Aksoy and Chen 1992, Date 1993 mainly differ from one another on how the cell face velocities and their corresponding pseudo velocities are approximated. A simple approach proposed in this study is to use the average pseudo velocities of the node.…”

Section: Non-staggered Simpler Algorithmmentioning

confidence: 99%

Measurement of pressure distribution from PIV experiments

Jaw

Chen

2009

J Vis

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In this study, a non-staggered grid SIMPLER pressure solution algorithm, which is able to produce correct pressure distribution directly if correct velocities are given, is proposed to solve the pressure distribution for PIV experiments. The cell face pseudo velocity required in the pressure equation is approximated by a simple linear average of the adjacent nodal pseudo velocities so that the velocity and pressure are collocated without causing the checkerboard pressure distribution problem. In addition, the proposed pressure solution algorithm has the features that upwind effects of the convective terms are considered, boundary conditions are not required, and the pressure distribution obtained can be used to correct the velocity field so that the continuity equation is satisfied. These features make the present algorithm a superior method to calculate the pressure distribution for PIV experiments. The pressure field solved is realistic and accurate. The proposed pressure equation solver is first calibrated with a two-dimensional cavity flow. It is found that the results are almost identical to the exact solution of the test flow. The algorithm is then applied to analyze a uniform flow past two side-by-side circular cylinders in a soap film channel. With the velocity and pressure distributions successfully measured, the structures of the complex shedding flow patterns are clearly manifested.

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“…Note also that, to prevent the checkerboard pressure distribution, cell face velocities cannot be determined directly from a linear interpolation of their neighboring nodal velocities, but have to be determined from the combination of interpolated velocities and discretization coefficients [1]. The solution procedures are exactly the same as the staggered grid algorithm except that the cell face pseudo-velocity is calculated from Eq.…”

Section: Ec ~Ppcmentioning

confidence: 99%

“…To implement an algorithm on a non-staggered grid, modified schemes which do not provoke the 'checkerboard problem' must be developed. At present, several SIMPLE-type non-staggered grid numerical algorithms have been proposed [1,7]. However, most of them have suffered the problems of slow convergence and numerical inaccuracy [2].…”

Section: Introductionmentioning

confidence: 99%

Development and application of a non‐staggered pace algorithm for the solution of incompressible Navier‐Stokes equations

Jaw

Hwang

1998

Journal of the Chinese Institute of Engineers

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In this study, a non-staggered PACE (Pressure Accurate Continuity Exact) algorithm for the solution of incompressible Navier-Stokes equations is proposed. Time accurate solutions are obtained at each time step using consistent, multi-step iterations of pressure solution and velocity corrections. From the computation of a square cavity flow with different Reynolds numbers, it was found that the proposed nonstaggered PACE algorithm consumes less computer memory and CPU time, has a smoother rate of convergence, and can predict incompressible flows as accurately as a well-established staggered SIMPLER algorithm. A non-staggered grid algorithm is easier to implement and is more favorable as body-fitted or three-dimensional computations are required.

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Numerical Solution of Navier-Stokes Equations With Nonstaggered Grids Using Finite Analytic Method

Cited by 21 publications

References 10 publications

Cell face velocity alternatives in a structured colocated grid for the unsteady Navier–Stokes equations

Cell face velocity alternatives in a structured colocated grid for the unsteady Navier–Stokes equations

Measurement of pressure distribution from PIV experiments

Development and application of a non‐staggered pace algorithm for the solution of incompressible Navier‐Stokes equations

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