Parallel Implicit Solution of 3-D Navier-Stokes Equations

Gülçat, Ülgen; Ünal, Vildan Üstoğlu

doi:10.1016/b978-044450680-1/50036-x

Cited by 3 publications

(7 citation statements)

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“…Reduction in grid points and in half‐bandwidths in parallelization is advantages in terms of computational time. Super linear speed‐ups were achieved (Gülcat and Unal, 2002; Unal and Gülcat, 2003).…”

Section: Introductionmentioning

confidence: 94%

“…Having obtained the correct Neumann boundary condition for each interface, equation (11)/equation (13) is solved via the direct solution method at each sub-domain, together with the correct interface conditions as done in Gülcat and Unal (2002) and Unal and Gülcat (2003). The computations involving an inner iterative cycle and outer time step HFF 23,4 advancements have to be performed in a parallel manner on each processor communicating with the neighbouring one.…”

Section: For the Momentum And Poisson Equationsmentioning

confidence: 99%

“…At the following time level, each slave processor solves equation (11)/equation (13) together with the correct Neumann condition of the previous time level, (∂y i /∂n i )=(−1) i −1 μ k on the interface, and the slave processor starts to solve unit problem together with the initial interface Neumann condition of (∂ x i o )/(∂n i )=(−1) i −1 w o , where w o = ϖ k −(y 2 o −y 1 o ) S j . Having obtained the correct Neumann boundary condition for each interface, equation (11)/equation (13) is solved via the direct solution method at each sub‐domain, together with the correct interface conditions as done in Gülcat and Unal (2002) and Unal and Gülcat (2003). The computations involving an inner iterative cycle and outer time step advancements have to be performed in a parallel manner on each processor communicating with the neighbouring one.…”

Section: Domain Decompositionmentioning

confidence: 99%

“…The numerical method is described. The calibration of the code is done (as an addition to the calibration studies including only the momentum equation in Gülcat and Unal (2000), Gülcat and Unal (2002) and Unal and Gülcat (2003) with the natural convection problem in cubic cavity. Since 2‐D problem results published by de Vahl Davis in 1983, a recent database search for the studies of “square cavity flow” yields 1,269 matches (Web of Science, 2011).…”

Section: Introductionmentioning

confidence: 99%

“…The pressure, on the other hand, is obtained by way of an auxiliary scalar potential which satisfies the Poisson's equation. For the parallel implicit solution to the matrix equations, domain decomposition method (Gülcat and Unal, 2000, 2002; Unal and Gülcat, 2003; Glowinski and Periaux, 1982; Dinh et al , 1992; Glowinski et al , 1995) is utilized and direct inversion in each domain is performed. Reduction in grid points and in half‐bandwidths in parallelization is advantages in terms of computational time.…”

Section: Introductionmentioning

confidence: 99%

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Parallel numerical solution of incompressible full Navier‐Stokes in 3‐D

Ünal

2013

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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Purpose -The purpose of this paper is to develop and test an implicit scheme, accurate to the second order, for solving full Navier-Stokes equations for three dimensional problems, using parallel algorithm. Design/methodology/approach -Parallel solution to the 3-D incompressible full Navier-Stokes equations is presented, based on two fractional steps in time and finite element in space. The accuracy of the scheme is second order in both time and space domains. Large time-step sizes, with Courant-Friedrichs-Lewy (CFL) numbers much larger than unity, are taken since the momentum equation is solved implicitly. A fourth order artificial viscosity term is added. In order to stabilize the numerical solution, fourth order artificial viscosity term is used for high Reynolds number flows. The domain decomposition technique is implemented for parallel solution to the problem with matching and non-overlapping sub-domains. It is aimed to study both a 3D free and mixed convection problems using the developed scheme. The segregate solution for temperature field is calibrated by a 3-D free convection problem. Then the flow case where the forced convection is one order of magnitude higher than the free convection is studied. Findings -It is observed that the long time solution to the flow field shows oscillatory behaviour as the Reynolds number of the flow doubled while keeping the ratio of the forced to free convection fixed. The solution using a parallel algorithm gives satisfactory results, in terms of computation time and accuracy, for the natural convection problem in cubic cavity, and, the forced cooling of a room with chilled ceiling having a parabolic geometry as presented at the end. It is observed that doubling the Reynolds number, while keeping all the parameters unchanged, varies the flow behaviour completely. Originality/value -A code previously developed and published by the author only solved momentum equation and studied the velocity field. In this study, full Navier Stokes equation is solved and the code is calibrated with a well-known 3D free-convection for two different Rayleigh number cases and then 3D mixed convection problem is studied for two cases. Re ¼ 2000 case results, solved both by the scheme in this study and by commercial code, presented an interesting physics of the problem. For Re ¼ 2000 case, continuous cooling of the room is not possible. Doubling the Reynolds number, raising it from 1000 to 2000, while keeping all the parameters unchanged, varies the flow behaviour completely.

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Section: Introductionmentioning

confidence: 94%

Section: For the Momentum And Poisson Equationsmentioning

confidence: 99%