A time accurate calculation procedure for flows with a free surface using a modified artificial compressibility formulation

Beddhu, Murali; Taylor, Lafayette K.; Whitfield, David L.

doi:10.1016/0096-3003(94)90164-3

Cited by 21 publications

(17 citation statements)

References 4 publications

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“…Many authors [7][8][9] have applied this method successfully. In addition, the ACM has been applied to free surface ows by a number of authors [10,11]. In this paper, we decompose the pressure into its hydrostatic and hydrodynamic parts, and the ACM is applied only to the hydrodynamic pressure.…”

Section: Introductionmentioning

confidence: 99%

Applications of the artificial compressibility method for turbulent open channel flows

Lee

Teubner

Nixon

et al. 2006

Numerical Methods in Fluids

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SUMMARYA three-dimensional (3-D) numerical method for solving the Navier-Stokes equations with a standard k-turbulence model is presented. In order to couple pressure with velocity directly, the pressure is divided into hydrostatic and hydrodynamic parts and the artiÿcial compressibility method (ACM) is employed for the hydrodynamic pressure. By introducing a pseudo-time derivative of the hydrodynamic pressure into the continuity equation, the incompressible Navier-Stokes equations are changed from elliptic-parabolic to hyperbolic-parabolic equations. In this paper, a third-order monotone upstreamcentred scheme for conservation laws (MUSCL) method is used for the hyperbolic equations. A system of discrete equations is solved implicitly using the lower-upper symmetric Gauss-Seidel (LU-SGS) method. This newly developed numerical method is validated against experimental data with good agreement.

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Section: Introductionmentioning

confidence: 99%

Applications of the artificial compressibility method for turbulent open channel flows

Lee

Teubner

Nixon

et al. 2006

Numerical Methods in Fluids

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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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“…According to this formulation the continuity equation is transformed from a constraint imposed on the velocity field to an evolution equation in time, by adding a time derivative of the pressure to it. The AC method, directly coupled with pressure and velocity field, was developed by Beddhu et al (1994), Li (2003), and Lee et al (2006).…”

Section: Introductionmentioning

confidence: 99%

Free Surface Flow in a Trench Channel Using 3-D Finite Volume Method

Lee¹,

Park²,

Oh³

2011

Journal of Korea Water Resources Association

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In order to simulate a free surface flow in a trench channel, a three-dimensional incompressible unsteady Reynolds-averaged Navier-Stokes (RANS) equations are closed with the    model. The artificial compressibility (AC) method is used. Because the pressure fields can be coupled directly with the velocity fields, the incompressible Navier-Stokes (INS) equations can be solved for the unknown variables such as velocity components and pressure. The governing equations are discretized in a conservation form using a second order accurate finite volume method on non-staggered grids. In order to prevent the oscillatory behavior of computed solutions known as odd-even decoupling, an artificial dissipation using the fluxdifference splitting upwind scheme is applied. To enhance the efficiency and robustness of the numerical algorithm, the implicit method of the Beam and Warming method is employed. The treatment of the free surface, so-called interface-tracking method, is proposed using the free surface evolution equation and the kinematic free surface boundary conditions at the free surface instead of the dynamic free surface boundary condition. AC method in this paper can be applied only to the hydrodynamic pressure using the decomposition into hydrostatic pressure and hydrodynamic pressure components. In this study, the boundary-fitted grids are used and advanced each time the free surface moved. The accuracy of our RANS solver is compared with the laboratory experimental and numerical data for a fully turbulent shallow-water trench flow. The algorithm yields practically identical velocity profiles that are in good overall agreement with the laboratory experimental measurement for the turbulent flow.

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A time accurate calculation procedure for flows with a free surface using a modified artificial compressibility formulation

Cited by 21 publications

References 4 publications

Applications of the artificial compressibility method for turbulent open channel flows

Applications of the artificial compressibility method for turbulent open channel flows

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

Free Surface Flow in a Trench Channel Using 3-D Finite Volume Method

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