On simulation of outflow boundary conditions in finite difference calculations for incompressible fluid

Olshanskii, Maxim A.; Staroverov, V. M.

doi:10.1002/1097-0363(20000630)33:4<499::aid-fld19>3.3.co;2-z

Cited by 14 publications

(17 citation statements)

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“…The formulation of outflow boundary conditions for the incompressible Navier-Stokes equations when computing either external or internal flows is still a subject of active research; see, for example, the work reported by Olshanskii and Staroverov [26], Hasan et al [27] and Nordstrom et al [28]. We have used, in the present work, the approximate boundary conditions (21) that assume that the flow is fully developed at the outlet section.…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…Keeping in mind the future applications that we have already referred to, we have implemented artificial dissipation terms in our numerical scheme. In particular, both second and fourth order terms have been used in the continuity equation (26), and fourth order terms in the momentum and energy equations (27)- (29). The implementation of these terms effectively changes the order of the equations (they cause them to become fourth order), so higher order boundary conditions are implemented for the artificial dissipation terms.…”

Section: Spatial and Temporal Discretisationmentioning

confidence: 99%

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Laminar heat transfer enhancement downstream of a backward facing step by using a pulsating flow

Velázquez

Arias

Méndez

2008

International Journal of Heat and Mass Transfer

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This study is motivated by the need to devise means to enhance heat transfer in configurations, like the back step, that appear in certain types of MEMS that involve fluid flow and that are not very efficient from the thermal transfer point of view. In particular, the work described in this paper studies the effect that a prescribed flow pulsation (defined by two control parameters: velocity pulsation frequency and pressure gradient amplitude at the inlet section) has on the heat transfer rate behind a backward facing step in the unsteady laminar 2-D regime. The working fluid that we have considered is water with temperature dependent viscosity and thermal conductivity. We have found that, for inlet pressure gradients that avoid flow reversal at both the upstream and downstream boundary conditions, the timeaveraged Nusselt number behind the step depends on the two above mentioned control parameters and is always larger than in the steady-state case. At Reynolds 100 and pulsating at the resonance frequency, the maximum time-averaged Nusselt number in the horizontal wall region located behind the step whose length is four times the step height is 55% larger than in the steady-case. Away from the resonant pulsation frequency, the time-averaged Nusselt number smoothly decreases and approaches its steady-state value.

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Section: Boundary Conditionsmentioning

confidence: 99%

Section: Spatial and Temporal Discretisationmentioning

confidence: 99%

Laminar heat transfer enhancement downstream of a backward facing step by using a pulsating flow

Velázquez

Arias

Méndez

2008

International Journal of Heat and Mass Transfer

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“…The above expressions are also obtained when directly applying to the momentum equations the scalings used to approximate the spatial Orr-Sommerfeld equations [11,17].…”

Section: Outflow Boundary Conditionsmentioning

confidence: 99%

A least-squares finite element formulation for unsteady incompressible flows with improved velocity–pressure coupling

Pontaza

2006

Journal of Computational Physics

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“…For the case of Oseenlinearized Navier-Stokes equations, Halpern and Schatzman [14] theoretically justified this approach as a transparent, local absorbing BC, when applying (13) for the streamwise component together with a zero gradient condition for the crossstream component. However, this behavior is not preserved in the non-linear case, as it was illustrated by Ol'shanskii and Staroverov [7] in their numerical experiments on perturbed channel flow, where they observed a notable upstream influence near the outflow of the domain. Fournier et al [15] argued that the observed contamination of the outflow region is mainly due to an overcorrection of the intermediate solution for the velocity in the pressure correction step, which is carried out in the fractionalstep based simulation of incompressible flow to enforce conservation of mass.…”

Section: Boundary Conditionsmentioning

confidence: 92%

“…Widely used standard outflow BCs like the von Neumann BC [4], or the convective outflow BC [7], are basically designed for parabolic flow, assuming a dominant downstream motion. These standard types of BC may lead to instabilities in the case of strongly buoyant jets.…”

Section: Introductionmentioning

confidence: 99%

Robust Outflow Boundary Conditions for Strongly Buoyant Turbulent Jet Flames

Walchshofer

Steiner

Brenn

2010

Flow Turbulence Combust

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The issue of prescribing open boundary conditions appropriate for highly transient flow simulations is a non-trivial one. It may have significant impact on the stability of the computations and the quality of the numerical results. The present paper proposes an outflow boundary condition which ensures stable simulations without significant losses in accuracy for use in direct numerical simulations of strongly buoyant turbulent jet flames. For the dynamic boundary condition, the proposed concept introduces a selective increase of the viscosity in the vicinity of the outflow. A uniform, steady-state flamelet solution is imposed to model the hydrodynamical effects of the flame, where a Robin-type boundary condition is applied for the mixture fraction at the outflow. The improved stability of the numerical solution is demonstrated by a comparison with a standard procedure using a purely advective boundary condition. Potential upstream effects of the proposed outflow boundary condition are investigated by computing two cases with different axial domain lengths. It could be clearly shown that the differences observed in the results for the two domain cases were not caused by the introduction of the additional viscosity at the outflow. They could be rather attributed to the prescription for the profile of the advective outflow velocity. Nomenclature Dimensional quantitiesD jet diameter, [m] g gravitational acceleration, m/s 2 μ j dynamic reference viscosity at nozzle conditions, kg/ms ρ j reference density at nozzle conditions, kg/m 3 U j reference velocity at nozzle, m/s Non-dimensionalized quantities and parameters a r streamwise advection term, a r = ∂ρu 2 ∂r

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On simulation of outflow boundary conditions in finite difference calculations for incompressible fluid

Cited by 14 publications

References 0 publications

Laminar heat transfer enhancement downstream of a backward facing step by using a pulsating flow

Laminar heat transfer enhancement downstream of a backward facing step by using a pulsating flow

A least-squares finite element formulation for unsteady incompressible flows with improved velocity–pressure coupling

Robust Outflow Boundary Conditions for Strongly Buoyant Turbulent Jet Flames

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