Accurate 3D viscous incompressible flow calculations with the FEM

Güļat, Ü.; Aslan, A. R.

doi:10.1002/(sici)1097-0363(19971115)25:9<985::aid-fld596>3.3.co;2-3

Cited by 3 publications

(7 citation statements)

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“…Instead of the explicit time‐marching scheme (Gülcat and Aslan, 1997), an implicit time‐marching scheme together with parallel algorithm and energy equation, is employed. The time integration of both sides of equation (4) for half a time step, Δ t /2, from time step n to n+1/2 gives: Equation 5 At the intermediate time step the time integration of equation (4), where the convective and viscous terms are taken at n+1/2 and pressure term at time level n, yields: Equation 6 For the full time step, the averaged value of the pressure and the temperature at time levels n and n+1 are used to give: Equation 7 Where the velocity is interpolated as follows: Equation 8 the indices i, j, and k denote the element node number: the summation convention is employed on repeated indices (in this case one‐eight), index e denotes the element number.…”

Section: Formulationmentioning

confidence: 99%

“…Subtracting equation (6) from equation (7) results in: Equation 9 If one takes the divergence of equation (8), the following is obtained: Equation 10 After subtracting equation (5) from equation (6), the integrand of the resulting equation reads (different than in Gülcat and Aslan (1997)): Equation 11…”

Section: Formulationmentioning

confidence: 99%

“…The space is discretized with Galerkin finite element method (Zienkiewicz and Taylor, 1989; Gunzburger, 1989; Hayashi et al , 1991; Marx, 1994; Despotis and Tsangaris, 1995; Utnes and Ren, 1995; Türek, 1996; Manzari, 2003; Donea and Huerta, 2003). The modified version of the two‐step fractional method is used in time discretization of the momentum equation (Chorin, 1968; Mizukami and Tsuchiya, 1984; Gülcat and Aslan, 1997). Zienkiewicz et al (1990) and Codina et al (1998) bring pressure stabilization for free but with the expense of introducing artificial boundary conditions for the pressure and Gauthier et al (2004) and Saleri and Veneziani (2005) use the approximations obtained by the inexact LU factorization as preconditioners for GMRES loop on the Navier‐Stokes operator.…”

Section: Introductionmentioning

confidence: 99%

“…In order to make the code more efficient for parallelization, a scheme, which uses a direct solution technique and implicit time‐marching, is preferred, instead of the scheme with element‐by‐element iterative solution technique and explicit time‐marching developed in Gülcat and Aslan (1997).…”

Section: Introductionmentioning

confidence: 99%

“…The implicit formulation for the momentum equation and the parallel implementation of the momentum, of the pressure and of the energy equation will be given in the following sections. In order to stabilize the numerical solution, fourth order artificial viscosity term is added for high Reynolds number flows, as done similarly in Gülcat and Aslan (1997) and Kallinderis and Nakajima (1994).…”

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: Formulationmentioning

confidence: 99%

Section: Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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Forced convection heat transfer from solder balls on a printed circuit board using the characteristic based split (CBS) scheme

Nithiarasu

Massarotti

Mathur

2005

Int Jnl of Num Meth for HFF

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PurposeTo numerically model forced convection heat transfer over arrays of solder balls.Design/methodology/approachThe characteristic based split (CBS) scheme has been used to solve the incompressible Navier‐Stokes equations on unstructured meshes.FindingsThe results show an increase in heat transport with increase in Reynolds numbers. A significant change in heat transfer is also noticed with change in angle of attack.Originality/valueThe presented results will be useful in designing cooling systems for electronic components.

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Forced convection heat transfer within a moderately‐stenosed, patient‐specific carotid bifurcation

Bevan

Lewis

Nithiarasu

2012

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

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Purpose -The purpose of this paper is to numerically model forced convection heat transfer within a patient-specific carotid bifurcation and to examine the relationship between the temperature and wall shear stress. Design/methodology/approach -The procedure employs a parallel, fully explicit (matrix free) characteristic based split scheme for the solution of incompressible Navier-Stokes equations. Findings -The arterial wall temperature, rather than the blood temperature dominates the regions of low wall shear stress and high oscillating shear stress. Additionally, negligible temperature gradient was detected proximal to the arterial wall in this locality. Originality/value -The presented results demonstrate a possible mechanism for cold air temperature to influence the atherosclerotic plaque region proximal to the stenosis. The proposed patient-specific heat transfer analysis also provides a starting point for the investigation of the influence of induced hypothermia on carotid plaque and its stability.

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Accurate 3D viscous incompressible flow calculations with the FEM

Cited by 3 publications

References 0 publications

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

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

Forced convection heat transfer from solder balls on a printed circuit board using the characteristic based split (CBS) scheme

Forced convection heat transfer within a moderately‐stenosed, patient‐specific carotid bifurcation

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