An upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations

Rogers, Stuart E.; Kwak, Dochan

doi:10.2514/6.1988-2583

Cited by 144 publications

(140 citation statements)

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“…These equations consist of a mass conservation WP5: Numerical Modelling CLASH -EVK3-CT-2001-00058 5 (density) equation (which is mathematically equivalent to the volume fraction transport equation), momentum equation and an incompressibility constraint that are solved simultaneously using the finite volume method. The formulation is based on the artificial compressibility method [51,52,53,54,36] in which the pressure, density and velocity fields are directly coupled to produce a hyperbolic system of equations. To achieve a time-accurate solution for unsteady flow problems an implicit dual-time iteration technique has been used [52,53] in which the solution at each real time step is obtained by solving a steady-state problem in a pseudo-time domain.…”

Section: Free Surface Capturing Methodsmentioning

confidence: 99%

Estudo do Galgamento de Estruturas Marítimas utilizando um Modelo Numérico baseado na Teoria da Onda em Condições de Água pouco Profunda

Reis¹,

Neves²

2010

RGCI

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The main objective of Workpackage 5 is to use numerical simulation of wave overtopping in order to solve the problem of suspected scale effects. A second, related, objective is to improve existing codes in such a way as they are able to simulate wave overtopping in a reliable way. The final, single, objective is to numerically model long waves on the shallow foreshore at Petten in order to understand the phenomenon of long waves and their effect on overtopping. This report deals with the work undertaken towards the first two objectives, the simulations undertaken for objective 3 are the subject of a separate report entitled "Influence of low-frequency waves on wave overtopping" by M.R.A. van Gent and C.C. Giarrusso and published by WL | Delft hydraulics in November 2003.Realistic simulations of wave overtopping require numerical methods which are able accurately to simulate the shoaling, breaking and possible overturning of waves prior to their impact on the seawall. It is a further requirement that the simulation continues after impact, modelling the formation of the overtopping jet and the reflection of the wave. The research groups at Manchester Metropolitan University (MMU) and the University of Gent (UGent) have been working in parallel on the development of such numerical codes. The MMU code, AMAZON-SC, is a numerical wave flume based on the free surface capturing approach. While the UGent code, LVOF, is a numerical wave basin based on the volume of fluid approach. This report describes the progress of these numerical methods, in order to address the first two objectives of Workpackage 5. Their application to various cases, is also discussed, including: a test problem involving wave overtopping of a smooth sea-dike, wave overtopping at Samphire Hoe and an investigation of scale effects on rough impermeable structures.The Report begins with a general introduction, followed by a section describing AMAZON-SC (the MMU code), a section describing LVOF (the UGent code) and then some general conclusions.

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Section: Free Surface Capturing Methodsmentioning

confidence: 99%

Estudo do Galgamento de Estruturas Marítimas utilizando um Modelo Numérico baseado na Teoria da Onda em Condições de Água pouco Profunda

Reis¹,

Neves²

2010

RGCI

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“…3a and 4, respectively. The grids used in this study were modeled after Rogers structured Chimera grids for multi-element airfoils [13,15]. The Chimera procedure utilizes an overlapping grid system to combine the different grids into a composite mesh.…”

Section: Grid Generation and Refinementmentioning

confidence: 99%

“…The incompressible Navier-Stokes code, INS2D-UP [13,15], was selected for this analysis. Compressibility effects were neglected due to the low freestream Mach numbers (M � "0.2) for an aircraft in landing configuration.…”

Section: Flow Solvermentioning

confidence: 99%

“…The former research, using an incompressible Navier-Stokes solver [13] and a Chimera grid scheme [14], has shown significant progress in the prediction of flow over multi-element airfoils and wings in high-lift take-off and landing configurations. Specifically, the lift behavior of twodimensional multi-element airfoils at various angles-of-attack up to stall has been accurately predicted with the INS2D-UP code [15]. The latter research applied the INS2D-UP code to investigate the effect of a Gurney flap on a NACA 4412 airfoil.…”

Section: Introductionmentioning

confidence: 99%

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Navier–Stokes analysis of lift-enhancing tabs on multi-element airfoils

Carrannanto

Storms²,

Ross

et al. 1998

Aircraft Design

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The flow over multi-element airfoils with flat-plate lift-enhancing tabs was numerically investigated. Tabs ranging in height from 0.25 to 1.25% of the reference airfoil chord were studied near the trailing edge of the main element. The two-dimensional numerical simulation employed an incompressible Navier-Stokes solver using a structured, embedded grid topology. The effects of various tabs were studied at a constant Reynolds number on a two-element airfoil with a slotted flap. Both computed and measured results indicated that a tab in the main-element cove improved the maximum lift and lift-to-drag ratio relative to the baseline airfoil without a tab. Computed streamlines revealed that the additional turning caused by the tab may reduce the amount of separated flow on the flap. A three-element airfoil was also studied over a range of Reynolds numbers, with computed results shown to be in good agreement with experimental data.

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“…We use the artificial compressibility method which was first developed by Chorin (1967) and since then has been developed by various researchers for the solution of steady and unsteady flow fields (e.g. Rogers et al, 1990;Rogers et al, 1991;Pappou and Tsangaris, 1997). Our time accurate solver utilizes hybrid meshes of triangles and quadrilaterals in 2D and tetrahedra, pyramids, prisms and hexahedra in 3D.…”

Section: Introductionmentioning

confidence: 99%

Artificial Compressibility 3-D Navier-Stokes Solver for Unsteady Incompressible Flows with Hybrid Grids

Vrahliotis

Pappou

Tsangaris

2012

Engineering Applications of Computational Fluid Mechanics

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An unsteady incompressible numerical method for the solution of Navier-Stokes equations is presented. The finite volume solver adopts the method of artificial compressibility, using an implicit dual time stepping scheme for time accuracy. The 2D solver operates on general hybrid meshes containing triangles and quadrilaterals, while the 3D solver operates on hybrid meshes containing tetrahedra, pyramids, prisms and hexahedra. The developed algorithms for spatial discretization and time integration are mesh transparent. An upwind spatial discretization scheme is used for the convective terms and a central scheme for the diffusive terms. Efficient calculation of flow fluxes is implemented in an edge-wise fashion. A new combined method for efficient and accurate evaluation of variable gradients is achieved by using an averaging technique and by avoiding multiple spatial integration of the same element of the mesh. The results obtained agree well with numerical solutions obtained by other researchers.

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An upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations

Cited by 144 publications

References 10 publications

Estudo do Galgamento de Estruturas Marítimas utilizando um Modelo Numérico baseado na Teoria da Onda em Condições de Água pouco Profunda

Estudo do Galgamento de Estruturas Marítimas utilizando um Modelo Numérico baseado na Teoria da Onda em Condições de Água pouco Profunda

Navier–Stokes analysis of lift-enhancing tabs on multi-element airfoils

Artificial Compressibility 3-D Navier-Stokes Solver for Unsteady Incompressible Flows with Hybrid Grids

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