Two-dimensional,high-resolution modeling of urban dam-break flooding: A case study of Baldwin Hills,California

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 1.5 m 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. 5 m 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.     

Efficient scheme for the shallow water equations on unstructured grids with application to the Continental Shelf

In this paper, a shallow-water flow solver is presented, based on the finite-volume method on unstructured grids The method is suitable for flows that occur in rivers, channels, sewer systems (1D), shallow seas, rivers, overland flow (2D), and estuaries, lakes and shelf breaks (3D). We present an outline of the numerical approach and show three 2D test cases and an application of tidal propagation on the Continental Shelf. The benefits of applying an unstructured grid were explored by creating an efficient model network that aims at keeping the number of grid cells per wavelength constant. The computational speed of our method was compared with that of WAQUA/TRIWAQ and Delft3D (the commonly used structured shallow-flow solvers in The Netherlands), and comparable performance was found.     

自适应非结构有限元MT二维起伏地形正反演研究

在山区进行MT勘探时,用规则网格有限元方法模拟起伏地形会受到限制.本文采用非结构三角网格可以有效地模拟任意二维地质结构,如起伏地形、倾斜岩层和多尺度构造等.正演引入自适应有限元方法,其在网格剖分过程中能根据单元误差自动细化网格,保证了正演结果的精度.将自适应有限元与Occam算法结合,且引用并行处理技术提高正反演计算速度.通过对比两个理论模型,讨论了地形对MT正演响应的影响;其次进行了不同地电模型带地形反演展示了本文算法的正确性和适用性;最后将该方法应用于实测MT数据处理,证明了自适应非结构有限元方法是复杂地形下处理MT数据的有力工具.     

Mesh grading approach for wave propagation in high velocity-contrast media

A mesh grading approach based on investigated lump method has been presented for simulating wave propagation in high velocity-contrast media. Unstructured fine grids are used to discretize the low wave-velocity medium in order to ensure the accuracy of numerical computation, and unstructured coarse grids are used for the high wave-velocity medium in order to substantially reduce the computational cost. On the interface, one coarse grid can match the fine grids of arbitrary odd number. The key feature of the proposed method is the constructions of investigated lumps on the interfaces of media. The transition zone, which is commonly used in the discontinuous grid scheme based on the staggered-grid finite-difference method, will not be used any more. Moreover, the computational instability that the discontinuous grid schemes frequently encountered does not arise in the proposed method. The comparisons with the analytical solutions and the application in studying the effects of sedimentary basin demonstrated that the mesh grading approach is a valid, accurate, convenient and flexible algorithm in simulating wave propagations in high velocity-contrast media with irregular interfaces.     

Finite element numerical simulation of 2.5D direct current method based on mesh refinement and recoarsement

To deal with the problem of low computational precision at the nodes near the source and satisfy the requirements for computational efficiency in inversion imaging and finite-element numerical simulations of the direct current method, we propose a new mesh refinement and recoarsement method for a two-dimensional point source. We introduce the mesh refinement and mesh recoarsement into the traditional structured mesh subdivision. By refining the horizontal grids, the singularity owing to the point source is minimized and the topography is simulated. By recoarsening the horizontal grids, the number of grid cells is reduced significantly and computational efficiency is improved. Model tests show that the proposed method solves the singularity problem and reduces the number of grid cells by 80% compared to the uniform grid refinement.     

ParBreZo: A parallel,unstructured grid,Godunov-type,shallow-water code for high-resolution flood inundation modeling at the regional scale

Topographic data are increasingly available at high resolutions (<10 m) over large spatial extents to support detailed flood inundation modeling and loss estimation analyses required for flood risk management. This paper describes ParBreZo, the parallel implementation of a two-dimensional, Godunov-type, shallow-water code, to address the computational demand of high-resolution flood modeling at the regional scale (10²–10⁴ km²). A systematic approach to unstructured grid partitioning (domain decomposition) is presented, and the Single Process Multiple Data (SPMD) paradigm of distributed-memory parallelism is implemented so the code can be executed on computer clusters with distributed memory, shared memory, or some combination of the two (now common with multi-core architectures). In a fully-wetted, load-balanced test problem, the code scales very well with a parallel efficiency of close to 100% on up to 512 processes (maximum tested). A weighted grid partitioning is used to partially address the load balancing challenge posed by partially wetted domains germane to flooding applications, where the flood extent varies over time, while the partitioning remains static. An urban dam-break flood test problem shows that weighted partitions achieve a parallel efficiency exceeding 70% using up to 48 processes. This corresponds to a 97% reduction in execution time so results are obtained in a matter of minutes, which is attractive for routine engineering analyses. A hurricane storm surge test problem shows that a 10 m resolution, 12 h inundation forecast for a 40 km length of coastline can be completed in under 2 h using 512 processors. Hence, if coupled to a hurricane forecast system capable of resolving storm surge, inundation forecasts could be made at 10 m resolution with at least a 10 h lead time.     

Unstructured mesh generation and landcover-based resistance for hydrodynamic modeling of urban flooding

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 5 m. 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.     

A 2D well-balanced shallow flow model for unstructured grids with novel slope source term treatment

Within the framework of the Godunov-type cell-centered finite volume (CCFV) scheme, this paper proposes a 2D well-balanced shallow water model for unstructured grids. In this model, the face-based van Albada limiting scheme is employed in conjunction with a directional correction to reconstruct second order spatial values at the midpoint of the considered face. The Harten, Lax and van Leer approximate Riemann solver with the Contact wave restored (HLLC) is applied to compute the fluxes of mass and momentum, while the splitting implicit method is utilized to solve the friction source terms. The novel aspects of the model include the new limited directional correction with which the new local extrema caused by the unlimited correction are prevented efficiently, the simplified non-negative water depth reconstruction used to get rid of numerical instabilities and in turn to preserve mass conservation at wet–dry interfaces and the novel slope source term treatment which suits complex unstructured grids well by transforming the slope source of a cell into fluxes at its faces. This model is able to preserve the C-property and mass conservation, to achieve good convergence to steady state, to capture discontinuous flows and to handle complex flows involving wetting and drying over uneven beds on unstructured grids with poor connectivity in an accurate, efficient and robust way. These capabilities are verified against analytical solutions, numerical results of alternative models and experimental and field data.     

Grid-size dependence of Cauchy boundary conditions used to simulate stream–aquifer interactions

This work examines the simulation of stream–aquifer interactions as grids are refined vertically and horizontally and suggests that traditional methods for calculating conductance can produce inappropriate values when the grid size is changed. Instead, different grid resolutions require different estimated values. Grid refinement strategies considered include global refinement of the entire model and local refinement of part of the stream. Three methods of calculating the conductance of the Cauchy boundary conditions are investigated. Single- and multi-layer models with narrow and wide streams produced stream leakages that differ by as much as 122% as the grid is refined. Similar results occur for globally and locally refined grids, but the latter required as little as one-quarter the computer execution time and memory and thus are useful for addressing some scale issues of stream–aquifer interactions. Results suggest that existing grid-size criteria for simulating stream–aquifer interactions are useful for one-layer models, but inadequate for three-dimensional models. The grid dependence of the conductance terms suggests that values for refined models using, for example, finite difference or finite-element methods, cannot be determined from previous coarse-grid models or field measurements. Our examples demonstrate the need for a method of obtaining conductances that can be translated to different grid resolutions and provide definitive test cases for investigating alternative conductance formulations.     

Development and evaluation of a local grid refinement method for block-centered finite-difference groundwater models using shared nodes

A new method of local grid refinement for two-dimensional block-centered finite-difference meshes is presented in the context of steady-state groundwater-flow modeling. The method uses an iteration-based feedback with shared nodes to couple two separate grids. The new method is evaluated by comparison with results using a uniform fine mesh, a variably spaced mesh, and a traditional method of local grid refinement without a feedback.Results indicate: (1) The new method exhibits quadratic convergence for homogenous systems and convergence equivalent to uniform-grid refinement for heterogeneous systems. (2) Coupling the coarse grid with the refined grid in a numerically rigorous way allowed for improvement in the coarse-grid results. (3) For heterogeneous systems, commonly used linear interpolation of heads from the large model onto the boundary of the refined model produced heads that are inconsistent with the physics of the flow field. (4) The traditional method works well in situations where the better resolution of the locally refined grid has little influence on the overall flow-system dynamics, but if this is not true, lack of a feedback mechanism produced errors in head up to 3.6% and errors in cell-to-cell flows up to 25%.     

基于WNAD方法的非一致网格算法及其弹性波场模拟

加权近似解析离散化(WNAD) 方法是近年发展的一种在粗网格步长条件下能有效压制数值频散的数值模拟技术. 在地震勘探的实际应用中, 不是所有情况都适合使用空间大网格步长. 为适应波场模拟的实际需要, 本文给出了求解波动方程的非一致网格上的WNAD算法. 这种方法在低速区、介质复杂区域使用细网格, 在其他区域采用粗网格计算. 在网格过渡区域, 根据近似解析离散化方法的特点, 采用了新的插值公式, 使用较少的网格点得到较高的插值精度. 数值算例表明, 非一致网格上的WNAD方法能够有效压制数值频散, 显著减少计算内存需求量和计算时间, 进一步提高了地震波场的数值模拟效率.     

Using the pseudospectral technique on curved grids for 2D acoustic forward modelling1

The Fourier pseudospectral method has been widely accepted for seismic forward modelling because of its high accuracy compared to other numerical techniques. Conventionally, the modelling is performed on Cartesian grids. This means that curved interfaces are represented in a ‘staircase fashion‘causing spurious diffractions. It is the aim of this work to eliminate these non-physical diffractions by using curved grids that generally follow the interfaces. A further advantage of using curved grids is that the local grid density can be adjusted according to the velocity of the individual layers, i.e. the overall grid density is not restricted by the lowest velocity in the subsurface. This means that considerable savings in computer storage can be obtained and thus larger computational models can be handled. One of the major problems in using the curved grid approach has been the generation of a suitable grid that fits all the interfaces. However, as a new approach, we adopt techniques originally developed for computational fluid dynamics (CFD) applications. This allows us to put the curved grid technique into a general framework, enabling the grid to follow all interfaces. In principle, a separate grid is generated for each geological layer, patching the grid lines across the interfaces to obtain a globally continuous grid (the so-called multiblock strategy). The curved grid is taken to constitute a generalised curvilinear coordinate system, where each grid line corresponds to a constant value of one of the curvilinear coordinates. That means that the forward modelling equations have to be written in curvilinear coordinates, resulting in additional terms in the equations. However, the subsurface geometry is much simpler in the curvilinear space. The advantages of the curved grid technique are demonstrated for the 2D acoustic wave equation. This includes a verification of the method against an analytic reference solution for wedge diffraction and a comparison with the pseudospectral method on Cartesian grids. The results demonstrate that high accuracies are obtained with few grid points and without extra computational costs as compared with Cartesian methods.     

Automatic Generation of Locally Refined Composite Grids for Efficient Solute Transport Modeling

Widely used numerical models of solute transport processes in subsurface aquifers are limited to nonlocally refined rectangular, or logically rectangular, structured grids. This presents an unsuitable option to efficient numerical simulations maintaining an acceptable level of accuracy. Optimal selection of locally refined cells for efficient solute transport models is challenging to the current generation of numerical models. We present a novel and relatively simple to implement algorithm addressing these shortcomings. This method operates in four steps involving travel times simulations, a grid coarsening stage followed by a selective local grid refinement based on a cell-wise indicator, and a final postprocessing step. The refinement index is the sum of weighted logarithmic distributions of scaled forward and backward travel times. We calculate representative flow and transport properties at the two scales of the composite grid with a flow-based upscaling technique. We present two test problems to demonstrate the performances of this new gridding algorithm. We obtain the most important speedups for composite grids generated with the highest indicator thresholds. When hydrodynamic dispersion effects increase, we obtain less important speedups. An important outcome of this work is that grid design depends on nature and strength of the underlying flow and solute transport processes. Therefore, we suggest developing solute transport workflows integrating this grid generation algorithm as an integral component to build comprehensive and efficient groundwater models.     

深度均匀采样梯形网格有限差分地震波场模拟方法

由于重力引起的岩石压实效应,一般来说,地震波传播速度由浅入深整体逐渐增大.梯形坐标系设计可耦合速度由浅入深逐渐增大的变化,该坐标系中均匀网格采样所对应的物理直角坐标系网格由浅入深逐渐增大,也即浅部低速区对应细网格,深部高速区对应粗网格.在梯形坐标系表征波动方程后利用有限差分求解,本文实现一种深度均匀采样、横向采样间隔随深度增加逐渐线性增大的有限差分地震波模拟方法.梯形坐标系波动方程离散后,仍采用常规均匀网格有限差分算法对其求解.由于横向网格大小由浅入深线性增加,本方法可避免不同大小网格区域过渡所产生的虚假反射.梯形坐标系波场模拟浅层精度高,深层横向响应范围广,可有效减少有限差分网格数量.本文提出的方法是在更广义的坐标系下利用有限差分求解波动方程,正交坐标系仅为该梯形坐标系之特例.本文旨在为大速度动态范围深地高效高精度地震波场模拟提供一种思路.     

A Cartesian cut cell method for shallow water flows with moving boundaries

A new computational method for the calculation of shallow water flows with moving physical boundaries is presented. The procedure can cope with shallow water problems having arbitrarily complex geometries and moving boundary elements. Although the method provides a fully boundary-fitted capability, no mesh generation is required in the conventional sense. Solid regions are simply cut out of a background Cartesian mesh with their boundaries represented by different types of cut cell. Moving boundaries are accommodated by up-dating the local cut cell information on a stationary background mesh as the boundaries move. No large-scale re-meshing is required. For the flow calculations, a multi-dimensional high resolution upwind finite volume scheme is used in conjunction with an efficient approximate Riemann solver at flow interfaces, and an exact Riemann solution for a moving piston at moving boundary elements. The method is validated for test problems that include a ship's hull moving at supercritical velocity and two hypothetical landslide events where material plunges laterally into a quiescent shallow lake and a fiord.     

Optimal use of high‐resolution topographic data in flood inundation models

In this paper we explore the optimum assimilation of high‐resolution data into numerical models using the example of topographic data provision for flood inundation simulation. First, we explore problems with current assimilation methods in which numerical grids are generated independent of topography. These include possible loss of significant length scales of topographic information, poor representation of the original surface and data redundancy. These are resolved through the development of a processing chain consisting of: (i) assessment of significant length scales of variation in the input data sets; (ii) determination of significant points within the data set; (iii) translation of these into a conforming model discretization that preserves solution quality for a given numerical solver; and (iv) incorporation of otherwise redundant sub‐grid data into the model in a computationally efficient manner. This processing chain is used to develop an optimal finite element discretization for a 12 km reach of the River Stour in Dorset, UK, for which a high‐resolution topographic data set derived from airborne laser altimetry (LiDAR) was available. For this reach, three simulations of a 1 in 4 year flood event were conducted: a control simulation with a mesh developed independent of topography, a simulation with a topographically optimum mesh, and a further simulation with the topographically optimum mesh incorporating the sub‐grid topographic data within a correction algorithm for dynamic wetting and drying in fixed grid models. The topographically optimum model is shown to represent better the ‘raw’ topographic data set and that differences between this surface and the control are hydraulically significant. Incorporation of sub‐grid topographic data has a less marked impact than getting the explicit hydraulic calculation correct, but still leads to important differences in model behaviour. The paper highlights the need for better validation data capable of discriminating between these competing approaches and begins to indicate what the characteristics of such a data set should be. More generally, the techniques developed here should prove useful for any data set where the resolution exceeds that of the model in which it is to be used. Copyright © 2002 John Wiley & Sons, Ltd.     

可变网格与局部时间步长的高阶差分地震波数值模拟

提高计算精度与效率是所有地震波正演方法所追求的目标.本文通过将变化的空间网格与变化的时间步长技术相结合,提出一种空间网格大小与时间步长均可任意变化的高阶有限差分模拟方法.一系列数值试验表明,该方法在保证模拟精度的同时,显著提高了模拟的效率.这种可变空间网格与局部时间步长的模拟方法,能够精细刻画含孔缝洞介质以及横向变化剧烈介质的微小结构,减小地震波模拟误差,提高介质细微结构情况下的地震波传播模拟精度与效率.     

面向目标自适应海洋可控源电磁三维矢量有限元正演

本文实现了一种面向目标自适应海洋可控源电磁三维矢量有限元方法.为满足三维复杂电性结构模拟的需求,网格剖分采用非结构化六面体.在组装刚度矩阵之后,形成的大型复数线性方程组分解为等价的实数形式,利用带预条件的广义最小残差法进行求解.在获得微分方程的解之后,为提高解的准确性,通过面向目标的自适应误差估计来指示网格细化,重点加密能使观测点数值模拟精度提高的网格.对于大规模三维数据,为了使模型空间的并行计算达到均衡负载的效果,我们使用METIS函数库来进行网格计算任务量的划分.最后,通过对比一维解析解与三维自适应矢量有限元计算结果,验证了程序的正确性;通过自适应过程中误差指示子的分布,验证了面向目标自适应的有效性;通过对三维复杂模型进行均衡负载下的并行计算,测试了程序的可扩展性.     

A Godunov-Type Scheme for Atmospheric Flows on Unstructured Grids: Euler and Navier-Stokes Equations

In recent years there has been a growing interest in using Godunov-type methods for atmospheric flow problems. Godunov's unique approach to numerical modeling of fluid flow is characterized by introducing physical reasoning in the development of the numerical scheme (van Leer, 1999). The construction of the scheme itself is based upon the physical phenomenon described by the equation sets. These finite volume discretizations are conservative and have the ability to resolve regions of steep gradients accurately, thus avoiding dispersion errors in the solution. Positivity of scalars (an important factor when considering the transport of microphysical quantities) is also guaranteed by applying the total variation diminishing condition appropriately. This paper describes the implementation of a Godunov-type finite volume scheme based on unstructured adaptive grids for simulating flows on the meso-, micro- and urban-scales. The Harten-Lax-van Leer-Contact (HLLC) approximate Riemann solver used to calculate the Godunov fluxes is described in detail. The higher-order spatial accuracy is achieved via gradient reconstruction techniques after van Leer and the total variation diminishing condition is enforced with the aid of slope-limiters. A multi-stage explicit Runge-Kutta time marching scheme is used for maintaining higher-order accuracy in time. The scheme is conservative and exhibits minimal numerical dispersion and diffusion. The subgrid scale diffusion in the model is parameterized via the Smagorinsky-Lilly turbulence closure. The scheme uses a non-staggered mesh arrangement of variables (all quantities are cell-centered) and requires no explicit filtering for stability. A comparison with exact solutions shows that the scheme can resolve the different types of wave structures admitted by the atmospheric flow equation set. A qualitative evaluation for an idealized test case of convection in a neutral atmosphere is also presented. The scheme was able to simulate the onset of Kelvin-Helmholtz type instability and shows promise in simulating atmospheric flows characterized by sharp gradients without using explicit filtering for numerical stability.     

A mixed-dimensional finite volume method for two-phase flow in fractured porous media

We present a vertex-centered finite volume method for the fully coupled, fully implicit discretization of two-phase flow in fractured porous media. Fractures are discretely modeled as lower dimensional elements. The method works on unstructured, locally refined grids and on parallel computers with distributed memory. An implicit time discretization is employed and the nonlinear systems of equations are solved with a parallel Newton-multigrid method. Results from two-dimensional and three-dimensional simulations are presented.