Numerical simulation of overflow at vertical weirs using a hybrid level set/VOF method

This paper presents the applications of a newly developed free surface flow model to the practical, while challenging overflow problems for weirs. Since the model takes advantage of the strengths of both the level set and volume of fluid methods and solves the Navier-Stokes equations on an unstructured mesh, it is capable of resolving the time evolution of very complex vortical motions, air entrainment and pressure variations due to violent deformations following overflow of the weir crest. In the present study, two different types of vertical weir, namely broad-crested and sharp-crested, are considered for validation purposes. The calculated overflow parameters such as pressure head distributions, velocity distributions, and water surface profiles are compared against experimental data as well as numerical results available in literature. A very good quantitative agreement has been obtained. The numerical model, thus, offers a good alternative to traditional experimental methods in the study of weir problems.     

Unstructured grid based 2-D inversion of VLF data for models including topography

We present a 2-D inversion code incorporating a damped least-squares and a minimum-model approach for plane wave electromagnetic (EM) methods using an adaptive unstructured grid finite element forward operator. Unstructured triangular grids permit efficient discretization of arbitrary 2-D model geometries and, hence, allow for modeling arbitrary topography. The inversion model is parameterized on a coarse parameter grid which constitutes a subset of the forward modeling grid. The mapping from parameter to forward modeling grid is obtained by adaptive mesh refinement. Sensitivities are determined by solving a modified sensitivity equation system arising from the derivative of the finite element equations with respect to the model parameters. Firstly, we demonstrate that surface topography may induce significant effects on the EM response and in the inversion result, and that it cannot be ignored when the scale length of topographic variations is in the order of magnitude of the skin depth. Secondly, the dependency of the inversion on the starting model is discussed for VLF and VLF-R data. Thirdly, we demonstrate the inversion of a synthetic data set obtained from a model with topography. Finally, the inversion approach is applied to field data collected in a region with undulating topography.     

A two dimensional hydrodynamic and sediment transport model for dam break based on finite volume method with quadtree grid

This study aims to develop a robust, accurate and computationally efficient hydrodynamic and sediment transport model for dam break flows. The two dimensional shallow water equations are resolved based on the finite volume method with an unstructured quadtree mesh. The sediment transport and bed evolution modules are coupled with hydrodynamic module to predict simultaneously the hydrodynamics, sediment concentrations and morphological changes. The interface flux is computed by the HLL approximate Riemann solver with second order accuracy. The effects of pressure and gravity are included in source term in this model, which can simplify the computation and eliminate numerical imbalance between source and flux terms. For dam break flows occurring in complicated geometries, the quadtree rectangular mesh is used to refine the interesting area and important part. The model is first verified against results from laboratory experiments, existing numerical models and real life case. It is then used to simulate dam break flows over a mobile bed to investigate the bed evolution. The results are compared with experimental data and field data with good agreement. The method is simple, efficient, and conservative. It shows promise for handling hydrodynamic simulation and sediment transport for a wide range of dam break flows.     

Mitigating horizontal divergence “checker-board” oscillations on unstructured triangular C-grids for nonlinear hydrostatic and nonhydrostatic flows

A complication of finite-volume triangular C-grid methods is the numerical emergence of horizontal divergence errors that lead to grid-scale oscillations in vertical velocity. Nonlinear feedback via advection of momentum can lead to numerical instability in velocity modes via positive feedback with spurious vertical velocities induced by horizontal divergence truncation error. Existing strategies to mitigate divergence errors such as direct divergence averaging and increased diffusion do not completely mitigate horizontal vertical velocity oscillations. We present a novel elliptic filtering approach to mitigate this spurious error and more accurately represent vertical velocities via improved calculation of horizontal divergences. These results are applied to laminar curved channel flows, demonstrating the applicability of the method to reproduce secondary flow features.     

A new efficient Eulerian–Lagrangian localized adjoint method for solving the advection–dispersion equation on unstructured meshes

A new and high efficient scheme is developed for the Eulerian–Lagrangian Localized Adjoint Method (ELLAM) to solve the Advection–Dispersion transport Equation (ADE) on unstructured triangular meshes. To obtain accurate results, the new method requires a very limited number of integration points (usually 1 per element).     

Volume rendering visualization of 3D spherical mantle convection with an unstructured mesh

We propose a new approach to utilize the algorithm of hardware-assisted visibility sorting (HAVS) in the 3D volume rendering of spherical mantle convection simulation results over unstructured grid configurations. We will also share our experience in using three different spherical convection codes and then taking full advantages of the enhanced efficiency of visualization techniques, which are based on the HAVS techniques and related transfer functions. The transfer function is a powerful tool designed specifically for editing and exploring large-scale datasets coming from numerical computation for a given environmental setting, and generates hierarchical data structures, which will be used in the future for fast access of GPU visualization facilities. This method will meet the coming urgent needs of real-time visualization of 3D mantle convection, by avoiding the demands of huge amount of I/O space and intensive network traffic over distributed parallel terascale or petascale architecture.     

Interactions between nonlinear water waves and non-wall-sided 3D structures

Interactions between water waves and non-wall-sided cylinders are analyzed based on velocity potential theory with fully nonlinear boundary conditions on the free surface and the body surface. The finite element method (FEM) is adopted together with a 3D mesh generated through an extension of a 2D Delaunay grid on a horizontal plane along the depth. The linear matrix equation for the velocity potential is constructed by imposing the governing equation and boundary conditions through the Galerkin method and is solved through an iterative method. By imposing the gradient of the potential equal to the velocity, the Galerkin method is used again to obtain the velocity field in the fluid domain. Simulations are made for bottom mounted and truncated cylinders with flare in a numerical tank. Periodic waves and wave groups are generated by a piston type wave maker mounted on one end of the tank. Results are obtained for forces, wave profiles and wave runups. Further simulations are made for a cylinder with flare subjected to forced motion in otherwise still open water. Results are provided for surge and heave motion in different amplitudes, and for a body moving in a circular path in the horizontal plane. Comparisons are made in several cases with the results obtained from the second order solution in the time domain.     

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.     

一种新的三维大地电磁积分方程正演方法

采用规则六面体单元和并矢Green函数奇异积分等效积分技术,已有的大地电磁积分正演方法具有不能有效模拟地下复杂地质体和计算精度偏低的缺点.本文提出了一种新的三维大地电磁积分方程正演技术,即采用四面体单元、解析的并矢Green函数奇异积分表达式,达到既能模拟地下复杂异常体,又能有效提高已有积分方程法计算精度的目的.首先,采用四面体网格技术离散地下复杂异常体,获得四面体单元上的大地电磁积分方程.然后,利用针对四面体单元开发的新的奇异值积分的解析表达式,准确计算线性方程中的并矢Green函数的奇异积分,从而获得精确的线性方程.借助于PARDISO高性能并行直接求解器,实现了三维大地电磁问题的高精度求解.最后,基于国际标准3D-1模型和六棱柱模型,通过与其他方法结果的对比分析,验证了本文方法的正确性、处理高电导率对比度的能力(1000:1)和处理复杂模型的能力.     

Hydrodynamic modeling of Changjiang Estuary: Model skill assessment and large-scale structure impacts

An unstructured grid, Finite Volume Coastal Ocean Model (FVCOM) is used to study hydrodynamics and large-scale structure impacts in Changjiang Estuary. Field measurements conducted after the construction of the large-scale channel-jetty system are used to assess numerical results. The agreements between simulated and measured water levels, depth-averaged current velocities and tidally averaged longitudinal salinity distributions are excellent, as indicated by predictive skills higher than 0.94. The predictive skills for time series of salinity show a large range, from 0.97 to 0.62, in different measurement locations. The impacts of two 50 km long jetties and tens of spurs on the estuarine circulations as well as salinity distribution are investigated using comparisons of numerical results with and without jetty structures. Results reveal that the jetty structures intensify currents in the navigation channel and generate strong shear and vortices in jetty-spur blocks, which enhance turbulent mixing and degrade salinity stratification in the channel. The large-scale structures not only affect the flow field in the northern passage, but also play an important role in redistributing freshwater runoff in the multi-channel system, resulting in estuary-scale adjustments of circulations and salinity distribution.