Numerical solution of the steady incompressible Navier—Stokes equations for the flow past a sphere by a multigrid defect correction technique

Juncu, Gheorghe; Mihail, R.

doi:10.1002/fld.1650110403

Cited by 45 publications

(22 citation statements)

References 17 publications

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“…The observed flow field is in accordance with the assumption that the effect of magnetic field is the small perturbation of zero field potential flow. In the case of 0 M = , the drag coefficient values are in good agreement with the earlier work [Fornberg (1988), Juncu et al (1990)]. The comparison of the drag coefficient values for 0 M = is given in Table 5 and the graph of Reynolds number versus drag coefficient is presented in figure 29.…”

Section: Resultssupporting

confidence: 87%

“…The comparison of the drag coefficient values for 0 M = is given in Table 5 and the graph of Reynolds number versus drag coefficient is presented in figure 29. Juncu et al(1990) 0.53 --- Figure 29. Reynolds number versus drag coefficient.…”

Section: Resultsmentioning

confidence: 99%

“…In order to achieve second order accurate solution, the defect correction method is employed as follows. With B as the operator obtained, for example, by first order upwind discretization and A is that obtained by second order accurate discretization, the defect correction algorithm (Juncu (1990) …”

Section: Methodsmentioning

confidence: 99%

“…The theoretical and experimental data presented in the literature (Clift et al, 1978) suggests that second order accuracy is at least desirable. We employed the defect correction technique (Juncu, 1990;Juncu et al, 1999) to obtain the second order accurate solution and it seems to be most adequate for the job.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Steady flow past a sphere in an aligned magnetic field at high Reynolds numbers

Kumar

Rajathy²

2014

Int. J. Eng. Sci. Tech

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The flow of steady, incompressible, viscous, electrically conducting fluid past a sphere in the presence of an uniform magnetic field parallel to the undisturbed flow is investigated using the finite difference method. The multigrid method with defect correction technique is used to achieve the second order accurate solution. The Hartmann number, M is used as the perturbation parameter. It is found that the increase of magnetic field decreases the wake length and increases the drag coefficient. The graphs of streamlines, vorticity lines, drag coefficient, surface pressure and surface vorticity are presented and discussed.

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Section: Resultssupporting

confidence: 87%

Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Steady flow past a sphere in an aligned magnetic field at high Reynolds numbers

Kumar

Rajathy²

2014

Int. J. Eng. Sci. Tech

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“…Approximating second order derivatives by central differences and convective terms by upwind scheme (UDS) prevents oscillations but reduces the order of accuracy to O(h). The results obtained by UDS can be extended to second order accuracy by applying defect correction technique (DC) [14]. In this study, the results are also simulated with UDS and DC techniques with a large domain of 120.023 times the radius of the cylinder and compared with HOCS.…”

Section: Resultsmentioning

confidence: 99%

Higher Order Compact Scheme Combined with Multigrid Method for Momentum, Pressure Poisson and Energy Equations in Cylindrical Geometry

Raju¹

2012

TONUMJ

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A higher-order compact scheme combined with the multigrid method is developed for solving Navier-Stokes equations along with pressure Poisson and energy equations in cylindrical polar coordinates. The convection terms in the momentum and energy equations are handled in an effective manner so as to get the fourth order accurate solutions for the flow past a circular cylinder. The superiority of the higher order compact scheme is clearly illustrated in comparison with upwind scheme and defect correction technique by taking a large domain. The developed scheme accurately captures pressure and velocity gradients on the surface when compared to other conventional methods. The pressure in the entire computational domain is computed and the corresponding fourth order accurate pressure fields are plotted. The local Nusselt number and mean Nusselt number are calculated and compared with available experimental and theoretical results.

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A multigrid procedure for three‐dimensional flows on non‐orthogonal collocated grids

Smith¹,

Cope²,

Vanka³

1993

Numerical Methods in Fluids

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SUMMARYThe development of a multigrid solution algorithm for the computation of three-dimensional laminar fully-elliptic incompressible flows is presented. The procedure utilizes a non-orthogonal collocated arrangement of the primitive variables in generalized curvilinear co-ordinates. The momentum and continuity equations are solved in a decoupled manner and a pressure-correction equation is used to update the pressures such that the fluxes at the cell faces satisfy local mass continuity. The convergence of the numerical solution is accelerated by the use of a Full Approximation Storage (FAS) multigrid technique. Numerical computations of the laminar flow in a 90" strongly curved pipe are performed for several finite-volume grids and Reynolds numbers to demonstrate the efficiency of the present numerical scheme. The rates of convergence, computational times, and multigrid performance indicators are reported for each case. Despite the additional computational overhead required in the restriction and prolongation phases of the multigrid cycling, the superior convergence of the present algorithm is shown to result in significantly reduced overall CPU times.

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Numerical solution of the steady incompressible Navier—Stokes equations for the flow past a sphere by a multigrid defect correction technique

Cited by 45 publications

References 17 publications

Steady flow past a sphere in an aligned magnetic field at high Reynolds numbers

Steady flow past a sphere in an aligned magnetic field at high Reynolds numbers

Higher Order Compact Scheme Combined with Multigrid Method for Momentum, Pressure Poisson and Energy Equations in Cylindrical Geometry

A multigrid procedure for three‐dimensional flows on non‐orthogonal collocated grids

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