Pressure Decimation and Interpolation (PDI) method for a baroclinic non-hydrostatic model

Shi, Jian; Shi, Fengyan; Kirby, James T.; Ma, Gangfeng; Wu, Guoxiang; Tong, Chaofeng; Zheng, Jinhai

doi:10.1016/j.ocemod.2015.09.010

Cited by 30 publications

(16 citation statements)

References 49 publications

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“…This observation, and inspired by the work of Van Reeuwijk (2002) and Shi et al (2015), motivates us to solve the vertical and horizontal momentum balances on essentially separate grids. The vertical balance (and pressure) is evaluated on a coarse grid of which the resolution is dictated by the wave motion, whereas the horizontal balance is solved on a finer grid to account for vertical shear.…”

Section: Introductionmentioning

confidence: 90%

Efficient non-hydrostatic modelling of 3D wave-induced currents using a subgrid approach

Rijnsdorp

Smit²,

Zijlema

et al. 2017

Ocean Modelling

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Wave-induced currents are an ubiquitous feature in coastal waters that can spread material over the surf zone and the inner shelf. These currents are typically under resolved in non-hydrostatic wave-flow models due to computational constraints. Specifically, the low vertical resolutions adequate to describe the wave dynamics-and required to feasibly compute at the scales of a field site-are too coarse to account for the relevant details of the three-dimensional (3D) flow field. To describe the relevant dynamics of both wave and currents, while retaining a model framework that can be applied at field scales, we propose a two grid approach to solve the governing equations. With this approach, the vertical accelerations and non-hydrostatic pressures are resolved on a relatively coarse vertical grid (which is sufficient to accurately resolve the wave dynamics), whereas the horizontal velocities and turbulent stresses are resolved on a much finer subgrid (of which the resolution is dictated by the vertical scale of the mean flows). This approach ensures that the discrete pressure Poisson equation-the solution of which dominates the computational effort-is evaluated on the coarse grid scale, thereby greatly improving efficiency, while providing a fine vertical resolution to resolve the vertical variation of the mean flow. This work presents the general methodology, and discusses the numerical implementation in the SWASH wave-flow model. Model predictions are compared with observations of three flume experiments to demonstrate that the subgrid approach captures both the nearshore evolution of the waves, and the wave-induced flows like the undertow profile and longshore current. The accuracy of the subgrid predictions is comparable to fully resolved 3D simulations-but at much reduced computational costs. The findings of this work thereby demonstrate that the subgrid approach has the potential to make 3D non-hydrostatic simulations feasible at the scale of a realistic coastal region.

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Section: Introductionmentioning

confidence: 90%

Efficient non-hydrostatic modelling of 3D wave-induced currents using a subgrid approach

Rijnsdorp

Smit²,

Zijlema

et al. 2017

Ocean Modelling

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“…Ma et al [41] extended the application of NHWAVE by considering the baroclinic pressure forcing in the momentum equation. To decrease the time consumed in solving the Poisson equation, Shi et al [42] added a pressure decimation interpolation (PDI) method into NHWAVE, which can greatly improve the model's efficiency without significantly impacting the model's accuracy obviously.…”

Section: Numerical Modelmentioning

confidence: 99%

Kelvin-Helmholtz Billows Induced by Shear Instability along the North Passage of the Yangtze River Estuary, China

Shi

Tong

Zheng

et al. 2019

JMSE

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Kelvin-Helmholtz (K-H) instability plays a significant role in mixing. To investigate the existence of K-H instability along the North Passage of the Yangtze River Estuary, the non-hydrostatic model NHWAVE is utilized to simulate the fresh-salt water mixing process along the North Passage of the Yangtze River Estuary. Using high horizontal resolution, the structure of K-H billows have been successfully captured within the Lower Reach of the North Passage. The K-H instability occurs between the max flood and high-water slack. The duration and length scale of the K-H billows highly depends on the local interaction between fresh-water discharge and tide. The horizontal length scale of the instability is about 60 m, similar to the observations in other estuaries. In the vertical direction, the K-H billows exist within the pycnocline with length scale ranging from 6 to 7 m. The timescale of the billows is approximate 6 min. By analyzing the changes of potential energy during the mixing process, results show that the existence of K-H instability induces intense vertical mixing, which can greatly increase mixing efficiency in the North Passage of the Yangtze River Estuary.Miles [10] and Howard [11] showed that a necessary condition for K-H instability in a parallel, stratified, inviscid flow, is that the gradient Richardson number (Ri = N 2 /S 2 , where N = −(g/ρ)(∂ρ/∂z) is the Brunt-Väisälä frequency, S = du/dz is the velocity shear, g is the gravity acceleration, ρ is density and u is a representative flow speed) is less than 0.25 somewhere in the flow. However, it has been demonstrated this criterion is not sufficient [12], because it is possible to have a stable shear layer when Ri < 0.25 at the pycnocline. Fringer and Street [13] found the interfacial wave can be stable with Ri < 0.25, but unstable perturbations occurred when Ri < 0.13. Barad and Fringer [14] used an adaptive numerical method to evaluate the critical Ri for instability, and the result showed a similar value of Ri < 0.1 is required for instability. Based on laboratory experiments, Fructus et al. [15] proposed a new criterion for instability, which is L x /λ > 0.86, where L x is the length of the region with Ri < 0.25 and λ is the wave width. Another alternative criterion for instability is based on the linear stability analysis with the Taylor-Goldstein equation. Troy and Koseff [16] used the equation to derive the criterion for instability, which requiresσ i T w > 5, where T w is the time the fluid spends in region with Ri < 0.25 andσ i is the averaged growth rate of the instabilities in the region.

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“…in which h(x, y) is water depth and η(x, y) is free surface elevation relative to still water level, (1) and (2) can be written in a compact, conservative form in the σ-coordinate (Shi et al, 2015):…”

Section: Governing Equationsmentioning

confidence: 99%

“…These simplifications also considerably reduce the computational requirements of the model. The Pressure Decimation and Interpolation (PDI) Method was added to NHWAVE by Shi et al (2015), who confirmed that the dynamic pressure can be modeled accurately with only a small number of vertical layers. This significantly increased model efficiency for simulating non-hydrostatic, baroclinic processes.…”

Section: Introductionmentioning

confidence: 95%

Incorporating floating surface objects into a fully dispersive surface wave model

et al. 2016

Self Cite

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The shock-capturing, non-hydrostatic, three-dimensional (3D) finite-volume model NHWAVE was originally developed to simulate wave propagation and landslide-generated tsunamis in finite water depth (Ma et al., 2012). The model is based on the incompressible Navier-Stokes equations, in which the z-axis is transformed to a σ-coordinate that tracks the bed and surface. As part of an ongoing effort to simulate waves in polar marginal ice zones (MIZs), the model has now been adapted to allow objects of arbitrary shape and roughness to float on or near its water surface. The shape of the underside of each floating object is mapped onto an upper σ-level slightly below the surface. In areas without floating objects, this σ-level continues to track the surface and bed as before. Along the sides of each floating object, an immersed boundary method is used to interpolate the effects of the object onto the neighboring fluid volume. Provided with the object's shape, location, and velocity over time, NHWAVE determines the fluid fluxes and pressure variations from the corresponding accelerations at neighboring cell boundaries. The system was validated by comparison with analytical solutions and a VOF model for a 2D floating box and with laboratory measurements of wave generation by a vertically oscillating sphere. A steep wave simulation illustrated the high efficiency of NHWAVE relative to a VOF model. In a more realistic MIZ simulation, the adapted model produced

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Pressure Decimation and Interpolation (PDI) method for a baroclinic non-hydrostatic model

Cited by 30 publications

References 49 publications

Efficient non-hydrostatic modelling of 3D wave-induced currents using a subgrid approach

Efficient non-hydrostatic modelling of 3D wave-induced currents using a subgrid approach

Kelvin-Helmholtz Billows Induced by Shear Instability along the North Passage of the Yangtze River Estuary, China

Incorporating floating surface objects into a fully dispersive surface wave model

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