Dissertation/Thesis Abstract

Three-dimensional, unstructured-grid numerical simulations of hydrodynamics and scalar transport in San Francisco Bay
by Chua, Vivien P., Ph.D., Stanford University, 2011, 164; 3497149
Abstract (Summary)

The unstructured-grid SUNTANS model is applied to San Francisco Bay and employed to perform three-dimensional simulations of flow in order to assess the performance of high- and low-order scalar transport schemes. The potential impacts of climate change are also studied. Using a grid with an average resolution of 50 m, the model accurately resolves tidal hydrodynamics in a domain that extends from the Pacific Ocean to the western portion of the Delta region, the flow through which is approximated with two rectangular boxes as a "false delta". A detailed calibration is performed, and we show that the model accurately predicts tidal heights, currents, and salinity at several locations throughout the Bay.

A sensitivity study is presented to understand the effects of grid resolution, the turbulence model, and the scalar transport scheme. Three levels of grid refinement are performed, and the results of a second-order accurate, TVD scalar transport scheme are compared to those with first-order upwinding. Our results show that the best convergence rate with respect to grid refinement occurs when the TVD scheme is employed. This accuracy degrades when the turbulence model is not employed due to a lack of feedback between vertical turbulent mixing and stratification. Significant horizontal diffusion associated with first-order upwinding eliminates the necessary horizontal salinity gradients required to induce baroclinic circulation and renders the results less sensitive to the turbulence model or grid refinement.

The quantification of numerical diffusion on unstructured grids when employing the finite-volume method is accomplished with a novel approach to analytically derive diffusion coefficients by extending the Hirt analysis on Cartesian grids to unstructured grids. Two forms of computing the modified equation termed the independent analysis and the combined analysis are employed. Numerical diffusion coefficients are overpredicted with the independent analysis which separately derives the modified equation for the two types of cells, while the combined analysis which employs a recurrence relation for one equation obtains the correct diffusion coefficients. The numerical diffusion coefficients are analytically derived for first-order upwinding and the second-order scheme which stabilizes central differencing but introduces dispersion. First-order upwinding is stable with the most restrictive Courant number constraint 0 ≤ C0 ≤ [special characters omitted]/2 ≈ 0.87 when &thetas; = π/6, while the second-order scheme is stable with 0 ≤ C0 ≤ 2/[special characters omitted] ≈ 0.82 for all &thetas;. An accuracy analysis shows that first-order upwinding is first-order accurate in time and space and the second-order scheme is second-order accurate in time and space.

An alternative domain-averaged formulation provides an estimate for numerical diffusion without the need for analytical methods. This formulation is particularly suited to compare the performance of high- and low-order scalar advection schemes for applications in complex geometries, and is applied to San Francisco Bay to assess the impact of tidal straining and time scales on numerical diffusion. Over long time-scales, the TVD scheme is less effective in regions of high tidal dispersion, since grid-scale variability resulting from strong straining of the tracer field causes strong numerical diffusion regardless of the method employed. For short time scales, the net diffusion coefficient is consistently smaller for the TVD scheme compared to first-order upwinding.

The unstructured-grid SUNTANS model is subsequently employed to investigate the implications of sea-level rise on salinity intrusion and estuarine circulation under different hydrologic scenarios in North San Francisco Bay. Rising sea levels reduce the impact of bottom-generated turbulence causing less vertical mixing. This leads to stronger gravitational circulation and higher vertical stratification, resulting in enhanced salinity intrusion. Under low-flow conditions, salinity intrusion is the largest because sea-level rise has a greater impact due to weaker vertical stratification. Strong flows increase the strength of the gravitational circulation, resulting in higher vertical stratification, which leads to the nonlinear feedback between vertical mixing and stratification. The effect of sea-level rise on vertical stratification and consequently salinity intrusion is reduced owing to the suppression of mixing by stratification.

Indexing (document details)
Advisor: Fringer, Oliver B.
School: Stanford University
School Location: United States -- California
Source: DAI-B 73/05, Dissertation Abstracts International
Subjects: Civil engineering, Ocean engineering, Environmental engineering
Keywords: Numerical diffusion, San Francisco Bay, Scalar transport scheme, Sea-level rise, Unstructured-grid
Publication Number: 3497149
ISBN: 9781267175199