Scott F. Bradford

Nonhydrostatic Model for Surf Zone Simulation

A previously developed model for nonhydrostatic free surface flow is adapted to simulate breaking waves in the surf zone. The model solves the Reynolds-averaged Navier-Stokes equations in a fraction step manner with the pressure split into hydrostatic and nonhydrostatic components. The hydrostatic equations are first solved with an approximate Riemann solver. This approach is particularly well suited for simulating discontinuous flow associated with breaking waves because the model prediction converges to the classical solution for a turbulent bore, which closely resembles breaking waves in the surf zone. The hydrostatic solution is then corrected by including the nonhydrostatic pressure. The model uses a sigma coordinate discretization in the vertical direction, which has been previously demonstrated to yield significant truncation errors with highly skewed grids over large bottom slopes. This potential problem is investigated in the context of highly skewed (but transient) grids that occur with steep br...

Network Implementation of the Two-Component Pressure Approach for Transient Flow in Storm Sewers

The two-component pressure approach (TPA) is an alternative to the Preissman slot method (PSM) for modeling highly transient sewer flow, including transitions between free-surface and pressurized conditions. TPA and PSM resolve intralink wave action by discretizing sewers with numerous elements and solving one-dimensional flow equations in contrast to link-node models, such as the popular storm water management model, which resolve only interlink wave action. Here, improvements of TPA are reported to support storm sewer network modeling. These include a source term discretization to preserve stationarity, a wetting and drying scheme, and a local time-stepping scheme to coordinate solution updates across many links and enable coupling to a two-dimensional overland flow model. A unique variant of the Harten, Lax and van Leer (HLL) Riemann solver is also introduced, and a boundary solver is developed to accommodate the wide range of possible flow regimes and transitions. The boundary solver is explicit to facilitate the extension of TPA to large networks and coupling with an overland flow model. Promising results are obtained in a varied set of test problems involving simple sewer networks.

The anti-dissipative, non-monotone behavior of Petrov-Galerkin upwinding

SUMMARY The Petrov‐Galerkin method has been developed with the primary goal of damping spurious oscillations near discontinuities in advection dominated flows. For time-dependent problems, the typical Petrov‐ Galerkin method is based on the minimization of the dispersion error and the simultaneous selective addition of dissipation. This optimal design helps to dampen the oscillations prevalent near discontinuities in standard Bubnov‐Galerkin solutions. However, it is demonstrated that when the Courant number is less than 1, the Petrov‐Galerkin method actually amplifies undershoots at the base of discontinuities. This is shown in an heuristic manner, and is demonstrated with numerical experiments with the scalar advection and Richards’ equations. A discussion of monotonicity preservation as a design criterion, as opposed to phase or amplitude error minimization, is also presented. The Petrov‐Galerkin method is further linked to the high-resolution, total variation diminishing (TVD) finite volume method in order to obtain a monotonicity preserving Petrov‐Galerkin method. Copyright

Modeling Flows with Moving Boundaries due to Flooding, Recession, and Wave Run-Up

Several free-surface flow problems involve the intermittent wetting and drying of arbitrary topography and simulating these processes is becoming increasingly important. For example, predictions of flooding due to a storm surge, breached dam, or overtopped levee are critical for disaster planning. Wave run-up estimates are needed for beach and coastal structure design. Descriptions of inundation, both in estuarine tidal flats and riverine flood plains, are key to predicting the transport of suspended and dissolved substances. Often such problems are modeled with depth-averaged flow equations that assume a hydrostatic pressure distribution. However, there are some instances where the flow is inherently three-dimensional and a depth-averaged treatment yields poor predictions. Therefore, an unsteady, three-dimensional model for free surface flow has been developed for simulating the wetting and drying of arbitrary terrain. The model is second-order accurate in space and time and is based on the finite volume method. Slope limiters are used to prevent the development of spurious oscillations at discontinuities. The model is applicable to both hydrostatic and nonhydrostatic flows. The standard k – ϵ turbulence model is employed to simulate breaking waves. Model predictions are compared with experimental data for nonlinear, solitary wave run-up on sloping beds. For weak nonlinearity, the hydrostatic model yields acceptable solution for run-up. However, for greater nonlinearity, the nonhydrostatic model yields a solution that more closely agrees with the data.

VERTICAL GRID DESIGN FOR MORE ACCURATE AND EFFICIENT SURF ZONE SIMULATION

Nonuniform vertical discretization is investigated for use with a previously developed numerical model that solves the incompressible, nonhydrostatic, Navier–Stokes equations for free surface flow. The equations are vertically transformed to the sigma coordinate system and solved in a fractional step manner in which the pressure is computed implicitly by correcting the hydrostatic flow field to be divergence free. A specific discretization is proposed to attain greater accuracy and/or minimize computational effort when compared to a uniform vertical discretization. Numerical accuracy is assessed by comparison with experimental data for spilling and plunging breakers.

Impact of high-resolution modeling on secondary flow phenomena

A high-resolution hydrodynamic model is used to demonstrate that small variations of coefficients in nonlinear filters used to preserve the monotonicity of the solution can lead to significant changes in the computed results. The model is applied to a complex geometry and bathymetry environment, which further aggravate the computational differences. Thermal plumes from hypothetical tests in Green Bay are shown to assume entirely different configurations following long runs of the model. The dissipative nature of various filters is found to alter dramatically not only the spurious oscillations, but the underlying smooth solution of the problem.