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Highlights • Detailed flood simulation for a whole city is achieved with parallel computing and upscaling. • Hourly flood simulations are completed in a matter of seconds to minutes. • Subcritical, supercritical and transcritical flows and compound flooding can be simulated. Abstract Simulation of flood inundation at metric resolution is important for making hazard information useful to a wide range of end-users involved in flood risk management, and addressing the alarming increase in flood losses that have been observed over recent decades. However, high data volumes and computational demands make this challenging over large spatial extents comparable to the metropolitan areas of major cities where flood impacts are concentrated, especially for time-sensitive applications such as forecasting and repetitive simulation for uncertainty assessment. Additionally, several factors present difficulties for numerical solvers including combinations of steep and flat topography that promote transcritical flows, the need to resolve flow in relatively narrow features such as drainage channels and roadways in urban areas which channel flood water during extreme events, and the need to depict compound hazards resulting from the interaction of pluvial, fluvial and coastal flooding. A new flood inundation model is presented here to address these challenges. The Parallel Raster Inundation Model (PRIMo) solves the shallow-water equations on an upscaled grid that is far coarser than the underlying raster digital topographic model (DTM), and uses a subgrid modeling approach so that the solution benefits from DTM-scale topographic data. Additionally, an approximate Riemann solver is applied in an innovative way to integrate fluxes between cells, as needed to update the solution by the finite volume method, which makes the method applicable to subcritical, supercritical and transcritical flows. PRIMo is implemented using a two-dimensional domain decomposition approach to Single Process Multiple Data (SPMD) parallel computing, and overlapping communications and computations are implemented to yield ideal parallel scaling for well-balanced test cases. With both a subgrid model and ideal parallel scaling, the model can scale to meet the demands of any application. Several benchmarks are presented to demonstrate predictive skill and the potential for timely, whole-city, metric-resolution flooding simulations. Limitations of the methods and opportunities for improvements are also presented. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: Urban flood inundation modeling with a hydrodynamic flow solver is addressed in this paper, focusing on strategies to effectively integrate geospatial data for unstructured mesh generation, building representation and flow resistance parameterization. Data considered include Light Detection and Ranging (LiDAR) terrain height surveys, aerial imagery and vector datasets such as building footprint polygons. First, a unstructured mesh-generation technique we term the building-hole method (BH) is developed whereby building footprint data define interior domain boundaries or mesh holes. A wall boundary condition depicts the impact of buildings on flood hydrodynamics. BH provides an alternative to the more commonly used method of raising terrain heights where buildings coincide with the mesh. We term this the building-block method (BB). Application of BH and BB to a flooding site in Glasgow, Scotland identifies a number of tradeoffs to consider at resolutions ranging from 1 to 5m. At fine resolution, BH is shown to be similarly accurate but execute faster than BB. And at coarse resolution, BH is shown to preserve the geometry of buildings and maintain better accuracy than BB, but requires a longer run time. Meshes that ignore buildings completely (no-building method or NB) also support surprisingly good flood inundation predictions at coarse resolution compared to BH and BB. NB also supports faster execution times than BH at coarse resolution because the latter uses localized refinements that mandate a greater number of computational cells. However, with mesh refinement, NB converges to a different (and presumably less-accurate) solution compared to BH and BB. Using the same test conditions, Hunter et al. [Hunter NM, Bates PD, Neelz S, Pender G, Villanueva I, Wright NG, Liang D, et al. Benchmarking 2D hydraulic models for urban flood simulations. ICE J Water Manage 2008;161(1):13–30] compared the performance of dynamic-wave and diffusive-wave models and reported that diffusive-wave models under-predicted the longitudinal penetration of the flood zone due to important inertial effects. Here, we find that a relatively coarse-mesh implementation of a dynamic-wave model suffers from the same drawback because of numerical diffusion. This shows that whether diffusion is achieved through the mathematics or numerics, the effect on flood extent is similar. Finally, several methods of distributing resistance parameters (e.g., Manning n) across the Glasgow site were evaluated including methods that utilize aerial imagery-based landcover classification data, MasterMap® landcover classification data and LiDAR-based feature height data (e.g., height of shrubs or hedges). Results show that landcover data is more important than feature height data in this urban site, that shadows in aerial imagery can cause errors in landcover classification which degrade flood predictions, and that aerial imagery offers a more detailed mapping of trees and bushes than MasterMap® which can locally impact depth predictions but has little impact on flood extent. [Copyright &y& Elsevier]

Summary: An integral form of the shallow-water equations suitable for urban flood modeling is derived by applying Reynolds transport theorem to a finite control volume encompassing buildings on a flood plain. The effect of buildings on storage and conveyance is modeled with a binary density function that equals unity when corresponds to a void, and nil otherwise, and can be measured using remote sensing data such as classified aerial imagery; the effect of buildings on flow resistance is modeled with a drag formulation. Discrete equations are obtained by applying the integral equations to a computational cell and adopting a Godunov-type, piecewise linear distribution of flow variables. The discrete equations include a volumetric porosity that represents the integral of over the cell, normalized by the cell area, and an areal porosity that represents the integral of over an edge of the mesh, normalized by the edge length. The latter is directionally dependent which introduces anisotropy to the shallow-water equations and captures sub-grid preferential flow directions which occur in urban settings due to asymmetric building shapes and spacings and the alignment of buildings along streets. A important implication is that model predictions are necessarily grid dependent; therefore, a mesh design strategy is proposed. First- and second-order accurate numerical methods are presented to solve the discrete equations, and applications are shown for verification and validation purposes including the ability of the model to resolve preferential flow directions. [Copyright &y& Elsevier]

Algebraic equations relating fluid volume and the free surface elevation in partially wetted quadrilateral computational cells are derived and incorporated into a Godunov-type, finite-volume, shallow-water model. These equations make it straightforward to reconstruct the free surface elevation based on the volume of fluid in a computational cell, the dependent variable tracked by finite volume models for conservation purposes, regardless of whether the cell is fully or partially wetted. Improvements to the variable reconstruction process streamline the computation of mass and momentum fluxes with approximate Riemann solvers, yielding a model that simulates sub-, super-, and transcritical flows over irregular topography with wetting and drying fronts. Furthermore, the model is free from fluid and scalar mass conservation errors and it eliminates nonphysical distributions of scalars by avoiding artificial concentration and/or dilution at wet/dry interfaces. Use of this wetting and drying methodology adds roughly 10% to the execution time of flow simulations. [ABSTRACT FROM AUTHOR]

A high-resolution, unstructured grid, finite-volume algorithm is developed for unsteady, two-dimensional, shallow-water flow and scalar transport over arbitrary topography with wetting and drying. The algorithm uses a grid of triangular cells to facilitate grid generation and localized refinement when modeling natural waterways. The algorithm uses Roe’s approximate Riemann solver to compute fluxes, a multidimensional limiter for second-order spatial accuracy, and predictor–corrector time stepping for second-order temporal accuracy. The novel aspect of the algorithm is a robust and efficient procedure to consistently track fluid volume and the free surface elevation in partially submerged cells. This leads to perfect conservation of both fluid and dissolved mass, preservation of stationarity, and near elimination of artificial concentration and dilution of scalars at stationary or moving wet/dry interfaces. Multi-dimensional slope limiters, variable reconstruction, and flux evaluation schemes are optimized in the algorithm on the basis of accuracy per computational effort. [ABSTRACT FROM AUTHOR]

Several techniques are investigated for extending Roe’s finite volume method to second-order spatial and temporal accuracy in order to better simulate shallow water flow over nonlevel beds. Specifically, methods reported in the literature for limiting and reconstructing dependent variables, discretizing source terms, and time stepping are examined. Steady subcritical and supercritical flow as well as unsteady flow over nonlevel beds is simulated in order to evaluate each methods’ performance in terms of error and computational effort. There is not a single method which minimizes error and computational effort for all test cases. On the contrary, methods that perform best in one application may be suboptimal in another. A general purpose modeling approach that balances accuracy against computational effort is identified and recommended. [ABSTRACT FROM AUTHOR]

Several finite-volume schemes are developed and applied to simulate nonlinear, dispersive, unidirectional waves propagating over a flat bed. These schemes differ mainly in the treatment of advection, while dispersion is treated the same among the different models. Three methods—linear, total variation diminishing, and essentially nonoscillatory—are used to discretize the advection portion of the governing equation. The linear schemes are analyzed with Von Neumann’s method to discern stability limits as well as their damping and dispersion characteristics. In addition, predictions from all of the models are compared with analytical solutions for solitary and cnoidal waves as well as experimental data for undular bores. The finite-volume methods are also compared with a second-order accurate finite-difference scheme. The results indicate that the finite-volume schemes yield more accurate solutions than the finite-difference scheme. In addition, the Warming-Beam and Fromm linear finite-volume schemes yielded the most accurate solutions and were among the most computationally efficient schemes tested. [ABSTRACT FROM AUTHOR]

Abstract: This work deals with the formulation and numerical implementation of a two-dimensional mathematical and numerical model describing open channel hydrodynamics, sediment and/or scalar transport and riverbed evolution in curved channels. It is shown that a well balanced 2D model can predict flow features, sediment and scalar concentration, and bed elevation with an accuracy that is suitable for practical river engineering. The term “balanced” implies that important physical processes are modeled with a similar degree of complexity and exhaustiveness. The starting point of the model formulation is the assumption of self-similarity of vertical velocity profiles (horizontal velocities in the longitudinal and transverse directions), that are scaled by shear velocity and streamline curvature, both resolved by the model. The former is scaled by a bed-resistance coefficient that must be estimated or calibrated – as usual – on a application-specific basis, and the latter is computed by a new, grid-based but grid orientation independent, scheme that acts on the discrete solution. All processes, including bottom shear, momentum dispersion, scalar dispersion, turbulent diffusion, bed load, and suspended load, are modeled using physically based, averaged values of empirical or semi-empirical constants, and consistently with the assumed velocity profiles (and bed-generated turbulence). Bed deformation modeling can be implemented with either an equilibrium or non-equilibrium formulation of the Exner equation, depending on the adaptation length scale, which must be taken under consideration if significantly larger than the length scale of the spatial discretization. The governing equations are solved by high-resolution, unstructured-grid Godunov method, which is elsewhere tested and shown to be reliable and second-order accurate. Application of the model to laboratory test cases, using standard parameter values and previously reported bed-resistance coefficients, gives results comparable to many 2D and 3D models previously applied to the same cases, most part of which benefit from case-specific parameter tuning. There are obviously intrinsic limits to the descriptive ability of 2D models in river modeling, but the results of this study point to the utility and cost-effectiveness of a well-designed 2D model. [Copyright &y& Elsevier]

Abstract: Modeling of dam-break flooding in an urban residential area in southern California is presented. Modeling is performed using BreZo, an unstructured grid, Godunov-type, finite volume model that solves the shallow-water equations. The model uses terrain data from a 1.5m Light Detection and Ranging (LiDAR) Digital Terrain Model (DTM) and contour data depicting the reservoir and breach geometry. A spatially distributed Manning coefficient based on a landcover classification derived from digital orthophotos and vector data (e.g., parcel outlines) is also used, and the interception of flow by storm drains is modeled with sink terms in the 2D continuity equation. The model is validated with flood extent and stream flow measurements, and a sensitivity analysis is completed to identify the necessary level of data and model complexity for accuracy purposes. Results show street depressions in the land surface should be resolved by the computational mesh for flood extent and stream flow accuracy. A ca. 5m resolution mesh that spans streets by approximately 3 cells achieves a good balance between accuracy and computational effort. Results also show that heterogeneous resistance is important for stream flow accuracy, and the interception of overland flow by storm sewers is important for flood extent accuracy. The sensitivity of predictions to several additional factors such as the reservoir level, breach geometry and DTM source (LiDAR, National Elevation Data, Shuttle Radar Topography Mission Data) is also reported. [Copyright &y& Elsevier]