An implicit three‐dimensional fully non‐hydrostatic model for free‐surface flows

Yuan, Hengliang; Wu, Chin H.

doi:10.1002/fld.778

Cited by 81 publications

(113 citation statements)

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“…Several flux-limiting schemes in combination with direction splitting techniques are used to calculate advection terms in scalar transport. Following standard procedures (Dee 1995, Roache 1998, the model has been carefully verified and validated with several free-surface flow problems Wu 2004, 2006;Yuan 2007). Also, we compared daily temperature profiles produced by the model to empirical temperature profiles collected by temperature loggers.…”

Section: Kamarainen Et Al Approaches For Estimating Entrainmentmentioning

confidence: 99%

“…The hydrodynamic model developed by Yuan and Wu (2004) and Wu et al (2008) employs the full Reynolds averaged Navier-Stokes equations, free of the hydrostatic pressure assumption that is commonly employed in other 3-D lake models (Hodges et al 2000, Rueda andSchladow 2003). This nonhydrostatic approach allows for more accurate simulation of dynamics that are important to solute transport and energy transfer in the lake such as internal wave evolution Street 2003, Venayagamoorthy andFringer 2005), flows…”

Section: Materials and Proceduresmentioning

confidence: 99%

“…Our intent is to present an assessment of the 3-D model as a tool in studying the physics of P recycling in a natural lake, rather than demonstrate validation of the model. Therefore, further technical details of the model and its verification and validation can be found in Wu (2004, 2006), Yuan (2007), and Wu et al (2008).…”

Section: Kamarainen Et Al Approaches For Estimating Entrainmentmentioning

confidence: 99%

“…3-D hydrodynamic model-We accounted for the full suite of dynamic processes using a 3-D hydrodynamic model (Yuan 2007 andWu et al 2008) for 6 days over the period from September 23 (day 266) to September 29 (day 272), 2005. This period was chosen due to high rates of entrainment and observed spatial heterogeneity.…”

Section: Materials and Proceduresmentioning

confidence: 99%

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Estimates of phosphorus entrainment in Lake Mendota: a comparison of one‐dimensional and three‐dimensional approaches

Kamarainen

Yuan

Carpenter

2009

Limnology & Ocean Methods

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Entrainment of phosphorus across the thermocline can be an important nutrient source for phytoplankton in stratified lakes. In eutrophic stratified lakes, seasonal entrainment can be responsible for delayed recovery following a decrease in external phosphorus load. We compared seasonal estimates of entrainment derived from single-and multilocation thermocline migration approaches. Entrainment estimates from these methods were similar. A sampling approach based on a single centralized location produced whole-lake entrainment estimates in general agreement with the mean value from the multilocation approach (the single-location approach reasonably reproduced patterns at a weekly and seasonal time scale). In this study, it was not essential to account for spatial variation in estimating annual rates of entrainment. We also estimated entrainment based on a threedimensional (3-D) hydrodynamic model over a short period of significant thermocline migration. The 3-D model was most useful in exposing spatial and temporal variation in temperature and phosphorus profiles that are otherwise difficult to observe. Spatial variation in phosphorus profiles was associated with upwelling of metalimnetic water represented by the 3-D model. These transient dynamics, though a relatively small portion of an annual phosphorus budget, may supply nutrients to epilimnetic phytoplankton during periods of nutrient limitation. There is a need for further research that combines 3-D hydrodynamic modeling with field collection of biological and chemical data.

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Section: Kamarainen Et Al Approaches For Estimating Entrainmentmentioning

confidence: 99%

Section: Materials and Proceduresmentioning

confidence: 99%

Section: Kamarainen Et Al Approaches For Estimating Entrainmentmentioning

confidence: 99%

Section: Materials and Proceduresmentioning

confidence: 99%

See 2 more Smart Citations

Estimates of phosphorus entrainment in Lake Mendota: a comparison of one‐dimensional and three‐dimensional approaches

Kamarainen

Yuan

Carpenter

2009

Limnology & Ocean Methods

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“…However, when the depth is small to be compared with the wave length, its assumption is not available for the abruptly changing bed topography, short wave motion, and the problem of the saltwater intrusion with strong density gradients. In recent years, the hydrodynamic models have been developed beyond limitations of the hydrostatic pressure assumption (Casulli and Stelling, 1998;Casulli, 1999;Stelling, 2001;Musteyde et al, 2002;Yuan and Wu, 2004;Lee et al, 2006a). A fractional step method, that the pressure is decomposed into the hydrostatic and the hydrodynamic pressure components, has been employed by Casulli and Stelling, Casulli, Stelling, Musteyde et al, Yuan and Wu, and Mahadevan et al. Because the hydrodynamic pressure component as a function of the velocity field in a fractional step method is unknown, an integrated time step using two fractional steps is employed for a fractional step method.…”

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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An implicit two‐dimensional non‐hydrostatic model for free‐surface flows

Ahmadi

Badiei

Namin

2006

Numerical Methods in Fluids

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An implicit finite volume model in sigma coordinate system is developed to simulate two-dimensional (2D) vertical free surface flows, deploying a non-hydrostatic pressure distribution. The algorithm is based on a projection method which solves the complete 2D Navier-Stokes equations in two steps. First the pressure term in the momentum equations is excluded and the resultant advection-diffusion equations are solved. In the second step the continuity and the momentum equation with only the pressure terms are solved to give a block tri-diagonal system of equation with pressure as the unknown. This system can be solved by a direct matrix solver without iteration. A new implicit treatment of non-hydrostatic pressure, similar to the lower layers is applied to the top layer which makes the model free of any hydrostatic pressure assumption all through the water column. This treatment enables the model to evaluate both free surface elevation and wave celerity more accurately. A series of numerical tests including free-surface flows with significant vertical accelerations and nonlinear behaviour in shoaling zone are performed. Comparison between numerical results, analytical solutions and experimental data demonstrates a satisfactory performance.A. AHMADI, P. BADIEI AND M. M. NAMIN computer power in recent years, three-dimensional (3D) models are extensively developed and applied for such problems. One of the main difficulties of such models is the proper handling of free surface moving boundary, especially for the cases such as short period waves. The moving free surface forms the upper boundary of the computational domain; however, its position also constitutes a part of the solution yet to be defined. In many 3D free-surface models, it is assumed that the vertical acceleration is small so that the idea of hydrostatic pressure can be applied. However, this statement is only applicable for simulating flows where the horizontal scale of motion is much larger than its vertical scale. For cases such as short period waves, rapidly changing bed topographies, and stratification due to strong density gradients, the hydrostatic pressure distribution is no longer valid and employing a dynamic pressure distribution, based on the complete form of NSE, is indispensable.In recent years, the development of non-hydrostatic models has been the topic of many research activities. Chorin [1] developed an explicit projection method that obtains the projected intermediate velocities after solving advection and diffusion terms explicitly at each time step, and then corrects the projected velocities by solving the pressure Poisson equation (PPE). Although the projection method may cause splitting errors in some applications [2], it has the advantage of using different schemes for different stages. Mahadevan et al. [3] proposed a non-hydrostatic ocean model using a semi-implicit control volume method. Stansby and Zhou [4] developed a two-dimensional (2D) vertical flow model for simulating the non-hydrostatic problem, using a semi-implicit time ...

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An implicit three‐dimensional fully non‐hydrostatic model for free‐surface flows

Cited by 81 publications

References 40 publications

Estimates of phosphorus entrainment in Lake Mendota: a comparison of one‐dimensional and three‐dimensional approaches

Estimates of phosphorus entrainment in Lake Mendota: a comparison of one‐dimensional and three‐dimensional approaches

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

An implicit two‐dimensional non‐hydrostatic model for free‐surface flows

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