Extending the MODPATH Algorithm to Rectangular Unstructured Grids

The recent release of MODFLOW‐USG, which allows model grids to have irregular, unstructured connections, requires a modification of the particle‐tracking algorithm used by MODPATH. This paper describes a modification of the semi‐analytical particle‐tracking algorithm used by MODPATH that allows it to be extended to rectangular‐based unstructured grids by dividing grid cells with multi‐cell face connections into sub‐cells. The new method will be incorporated in the next version of MODPATH which is currently under development.     

A Godunov-Type Scheme for Atmospheric Flows on Unstructured Grids: Scalar Transport

This is the first paper in a two-part series on the implementation of Godunov-type schemes on unstructured grids for atmospheric flow simulations. Construction of a high-resolution flow solver for the scalar transport equation is described in detail. Higher-order accuracy in space is achieved via a MUSCL-type gradient reconstruction after van Leer and the monotonicity of solution is enforced by slope limiters. Accuracy in time is maintained by implementing a multi-stage explicit Runge-Kutta time-marching algorithm. The scheme is conservative and exhibits minimal numerical dispersion and diffusion. Five different benchmark test cases are simulated for the validation of the numerical scheme.     

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.     

An Efficient and Robust Tsunami Model on Unstructured Grids. Part I: Inundation Benchmarks

A modern multi-purpose baroclinic circulation model (SELFE) has been recently extended to include the ability to simulate tsunami propagation and inundation. The core model is based on the 3-D nonlinear shallow-water wave (NSW) equations, which are solved on unstructured grids, using the finite-element method. A semi-implicit method is used to solve all equations to enhance numerical stability, thus bypassing the most stringent CFL restriction on the time step. Further aided algorithmically by an Eulerian-Lagrangian solution of the advection terms in the momentum equation and by a simple yet effective inundation algorithm, SELFE is very efficient and robust in both quasi-2-D (with two vertical layers) and 3-D modes. A quasi-2-D version of the model is being used to update and expand the characterization of tsunami hazards along the Oregon coast. As a part of a rigorous testing procedure that includes multiple types of coastal problems, we present in this paper a quantitative assessment of performance of the quasi-2-D SELFE for two challenging open benchmark problems proposed in the 3^rd International Workshop on Long-wave Runup Models. Satisfactory results are obtained for both problems.     

Unstructured Gridding for MODFLOW from Prior Groundwater Flow Models: A New Paradigm

This work introduces a new unstructured gridding approach relying on feedback from a previous groundwater flow model. All cells in a relatively coarse model using a rectilinear grid are recursively subdivided following a cell wise specific discharge-based indicator to generate quadtree, octree or Voronoï grids. This technique leverages the full potential of the latest MODFLOW engines. The suitability of this approach is demonstrated on challenging single and multilayered heterogeneous formations. The proposed method is straightforward to implement in existing software packages. It supports iterative updating of groundwater flow models from the legacy rectilinear to unstructured grids.     

Travel Time Distributions Derived from Particle Tracking in Models Containing Weak Sinks

A travel time distribution based on a particle-tracking analysis in a ground water model containing weak sinks is often uncertain because whether a particle is discharged or allowed to pass through a weak sink is unresolved by particle-tracking theory. We present a probability-based method to derive an objective travel time distribution in models containing weak sinks. The method discharges a fraction of the particle at the weak sink and allows the remaining fraction to pass through the weak sink. The weight of the discharged fraction depends on the ratio of the sink flux to the influx into the weak sink cell. We tested this approach on a coarse (100 × 100 m) and a fine (25 × 25 m) horizontal resolution regional scale ground water model (34.5 × 24 km). We compared the travel time distributions in a small subcatchment derived from particle-tracking analysis with one derived from a transport model. We found that the particle-tracking analysis with the coarse model underestimated the travel time distribution of the catchment compared to the transport solution or a particle-tracking analysis with the fine model. The underestimation of travel times with the coarse model was a result of a large area covered by sink cells in this model and the more accurate flow patterns simulated by the fine model. The probability-based method presented here compares favorably with a solute transport solution and provides an accurate travel time distribution when used with a fine-resolution ground water model.     

Modeling of Contaminant Movement Near Pumping Wells: Saturated-Unsaturated Flow with Particle Tracking

A transient axisymmetric saturated-unsaturated numerical flow model was coupled with a particle tracking model to investigate the movement of contaminants when a shallow unconfined aquifer is pumped at a constant rate. The particle tracking model keeps track of locations and masses of solutes in the aquifer, and the time of capture by the well. At the end of each time-step the flow model solves the Richard's equation for the hydraulic head distribution from which elemental velocities are calculated. Solutes are then displaced for a period equivalent to the time-step using both the magnitude and direction of the elemental velocities. Numerical experiments were performed to investigate effluent concentrations in wells with screens of different length and in different positions relative to zones of stratified contamination. At early times of pumping the effluent concentrations were similar to the concentrations adjacent to the well screen, but at late times, the concentrations approached the vertically averaged concentration in the aquifer. Time to attain the vertically averaged concentration was determined by the well geometry, initial location of the contaminant plume in relation to the well screen, and hydraulic properties of the aquifer. The results are consistent with the hydraulics of flow to a pumping well and of particular importance, they demonstrate that short-term pump tests could give erroneous design concentrations for pump-and-treat systems. The model provides a means of quantifying arrival times and mixing ratios. It could therefore provide a useful means of designing production wells in aquifers with stratified contamination and more efficient recovery systems for aquifer remediation.     

FloPy Workflows for Creating Structured and Unstructured MODFLOW Models

FloPy is a Python package for creating, running, and post-processing MODFLOW-based groundwater flow and transport models. FloPy functionality has expanded to support the latest version of MODFLOW (MODFLOW 6) including support for unstructured grids. FloPy can simplify the process required to download MODFLOW-based and other executables for Linux, MacOS, and Windows operating systems. Expanded FloPy capabilities include (1) full support for structured and unstructured spatial discretizations; (2) geoprocessing of spatial features and raster data to develop model input for supported discretization types; (3) the addition of functionality to provide direct access to simulated output data; (4) extension of plotting capabilities to unstructured MODFLOW 6 discretization types; and (5) the ability to export model data to shapefiles, NetCDF, and VTK formats for processing, analysis, and visualization by other software products. Examples of using expanded FloPy capabilities are presented for a hypothetical watershed. An unstructured groundwater flow and transport model, with several advanced stress packages, is presented to demonstrate how FloPy can be used to develop complicated unstructured model datasets from original source data (shapefiles and rasters), post-process model results, and plot simulated results.     

A Hamiltonian Particle Method with a Staggered Particle Technique for Simulating Seismic Wave Propagation

We present a Hamiltonian particle method (HPM) with a staggered particle technique for simulating seismic wave propagation. In the conventional HPM, physical variables, such as particle displacement and stress, are defined at the center, i.e., at the same position, of each particle. As most seismic simulations using finite difference methods (FDM) are practiced with staggered grid techniques, we know the staggered alignment of space variables could improve the numerical accuracy. In the present study, we hypothesized that staggered technique could improve the numerical accuracy also in the HPM and tested the hypothesis. First, we conducted a plane wave analysis for the HPM with the staggered particles in order to verify the validity of our strategy. The comparison of grid dispersion in our strategy with that in the conventional one suggests that the accuracy would be improved dramatically by use of the staggered technique. It is also observed that the dispersion of waves is dependent on the propagation direction due to the difference in the average spacing of the neighboring two particles for the same parameters, as is usually observed in FDM with a rotated staggered grid. Next, we compared the results from the conventional Lamb’s problem using our HPM with those from an analytical approach in order to demonstrate the effectiveness of the staggered particle technique. Our results showed better agreement with the analytical solutions than those from HPM without the staggered particles. We conclude that the staggered particle technique would be a method to improve the calculation accuracy in the simulation of seismic wave propagation.     

基于微粒群算法对城乡应急避难场所规划的研究

地震是具有毁坏性的自然灾害,对于震后严重受损的地区,设计合理的应急避难场所是非常必要的,为此提出基于微粒群算法对城乡应急避难场所规划的研究。将退火算法的微粒群理论与城乡地区应急避难场所规划相结合,在约束条件较多的情况下,将应急避难场所视为一个粒子,对应急避难场所规划创建目标函数,从而实现对城乡住区应急避难场所的规模规划设计;其次设计应急场所的内容与位置模型,集合城乡需求点布局的影响因素,修建不同的应急场所设施点,并以覆盖全部需求点为目标,实现应急避难场所的整体规划。通过仿真实验证明,所提微粒群算法具有较好的规划效率,可保证规划后的城乡住区在受到地震侵害后,受灾人群有即时的可避难场所,为人们的震后生活提供帮助。     

Unstructured grid generation using LiDAR data for urban flood inundation modelling

Inundation disasters, caused by sudden water level rise or rapid flow, occur frequently in various parts of the world. Such catastrophes strike not only in thinly populated flood plains or farmland but also in highly populated villages or urban areas. Inundation of the populated areas causes severe damage to the economy, injury, and loss of life; therefore, a proper management scheme for the disaster has to be developed. To predict and manage such adversity, an understanding of the dynamic processes of inundation flow is necessary because risk estimation is performed based on inundation flow information. In this study, we developed a comprehensive method to conduct detailed inundation flow simulations for a populated area with quite complex topographical features using LiDAR (Light Detection and Ranging) data. Detailed geospatial information including the location and shape of each building was extracted from the LiDAR data and used for the grid generation. The developed approach can distinguish buildings from vegetation and treat them differently in the flow model. With this method, a fine unstructured grid can be generated representing the complicated urban land features precisely without exhausting labour for data preparation. The accuracy of the generated grid with different grid spacing and grid type is discussed and the optimal range of grid spacing for direct representation of urban topography is investigated. The developed method is applied to the estimation of inundation flows, which occurred in the basin of the Shin‐minato River. A detailed inundation flow structure is represented by the flow model, and the flow characteristics with respect to topographic features are discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

基于微粒群算法的供水管网抗震优化设计

以管网年费用折算值为优化目标、管网拓扑结构与管径为优化参数、管网节点最低可靠度为约束条件,建立了供水管网抗震优化设计模型。利用微粒群算法对这一模型进行了求解,该算法以管网作为微粒个体,通过不断地更新微粒的位置来搜索最优的管网结构,直到最后给出优化的管网结构。利用上述方法对一典型供水管网进行了抗震优化设计分析,给出了3种不同节点最低可靠度约束条件下的优化改造方案。     

Parallel Visualization of Large-scale Unstructured Geophysical Data for the Earth Simulator

— A scalable and high-performance parallel visualization subsystem has been developed in GeoFEM for the Earth Simulator. As part of the Earth Simulator project in Japan, the proposed subsystem is effective for the visualization of large-scale geoscientific data, and can be concurrent with computation subsystems on the same high-performance parallel computer. Moreover, several parallel visualization methods are developed for large unstructured datasets, covering scalar, vector and tensor fields. Furthermore, a number of strategies are adopted in order to improve the parallel performance of the proposed subsystem for the Earth simulator, including the three-level hybrid parallelization and dynamic load balancing. Good visualization images and high parallel performance have been obtained on a Hitachi SR8000 for large unstructured geoscientific data sets, and thus demonstrating the feasibility and effectiveness of the proposed method for use on the Earth Simulator.     

基于非结构双网格的2D RMT双参数同步反演研究

Radio-magnetotelluric（RMT）是以无线电发射机为信号源的一种地球物理勘探方法,近年来被广泛应用于数米至数十米内的近地表工程和环境地球物理勘探.目前,各类电磁资料的反演均是以寻求满足目标拟合差的地下介质电阻率分布为目的.然而,对于勘探频率为10~300 kHz的RMT数据,由介电常数所引起的波动场在总场中的比例可达20%以上,在这种情况下,忽略介电常数,仅通过电阻率参数的反演来进行数据拟合势必降低反演资料解释的准确性.为解决这一问题,本文研究了基于电阻率-介电常数的双参数同步反演算法.构建了一个全新的双参数目标函数,并推导了双参数反演迭代方程组;通过灵敏度分析,研究了电阻率和介电常数对正演响应的影响,并据此提出相对电导率的概念,统一了反演参数的灵敏度;通过理论模型分析了参考频率、双参数正则化因子对反演结果的影响,并给出了一般性的参数优选方案.此外,为了能够灵活处理复杂地形,本文采用非结构的正反演双网格进行模型离散,并通过局部加密技术保证反演的速度和精度.最后,对一带地形的理论模型分别进行了单参数和双参数反演,结果表明单参数反演无法正确反映出地电信息,而双参数反演能够准确得到异常的分布,验证了本文所开发的双参数反演程序的有效性.

     

G-S变换的快速算法

在电磁场瞬变响应的数值计算中 ,常采用G S变换法作逆拉氏变换 .它是纯实数运算 ,而且只需对较少的拉氏变换变量s值作计算 （通常对每一采样时间选用 1 2个s值 ） ,因而是一种计算速度较快的算法 .但是 ,要对大量采样时间作计算 ,其计算量仍太大 .本文基于拉氏变换的延迟定理 ,建立了一种新的G S变换算法 .数值检验结果表明 ,新算法可成级次地减少对大量采样时间作G S变换的计算量 ,显著提高电磁场瞬变响应的计算速度 .