Comparison of free-surface and rigid-lid finite element models of barotropic instabilities

The main goal of this work is to appraise the finite element method in the way it represents barotropic instabilities. To that end, three different formulations are employed. The free-surface formulation solves the primitive shallow-water equations and is of predominant use for ocean modeling. The vorticity–stream function and velocity–pressure formulations resort to the rigid-lid approximation and are presented because theoretical results are based on the same approximation. The growth rates for all three formulations are compared for hyperbolic tangent and piecewise linear shear flows. Structured and unstructured meshes are utilized. The investigation is also extended to time scales that allow for instability meanders to unfold, permitting the formation of eddies. We find that all three finite element formulations accurately represent barotropic instablities. In particular, convergence of growth rates toward theoretical ones is observed in all cases. It is also shown that the use of unstructured meshes allows for decreasing the computational cost while achieving greater accuracy. Overall, we find that the finite element method for free-surface models is effective at representing barotropic instabilities when it is combined with an appropriate advection scheme and, most importantly, adapted meshes.     

Experiment and simulation of turbulent flow in local scour around a spur dyke

The turbulent flow in the local scour hole around a single non-submerged spur dyke is investigated with both experimental and numerical methods. The experiments are conducted under clear-water scour regime with an impermeable spur dyke. The scour geometry and flow velocities are measured in details with a high-resolution laser displacement meter, electro-magnetic velocimetries and PIV （Particle image velocimetry）. A 3D non-linear k-ε model is developed to simulate the complex local flow field around the scour area. The numerical model is formulated using FVM （Finite volume method） on a collocated unstructured mesh, capable of resolving complex geometries and boundaries. It is found that the simulation results are reasonably consistent with those of the experimental measurements. Based on the study results, the nature of the flow structure around a spur dyke with local scour hole is analyzed.     

Discontinuous Galerkin methods for advective transport in single-continuum models of fractured media

Accurate simulation of flow and transport processes in fractured rocks requires that flow in fractures and shear zones to be coupled with flow in the porous rock matrix. To this end, we will herein consider a single-continuum approach in which both fractures and the porous rock are represented as volumetric objects, i.e., as cells in an unstructured triangular grid with a permeability and a porosity value associated with each cell. Hence, from a numerical point of view, there is no distinction between flow in the fractures and the rock matrix. This enables modelling of realistic cases with very complex structures. To compute single-phase advective transport in such a model, we propose to use a family of higher-order discontinuous Galerkin methods. Single-phase transport equations are hyperbolic and have an inherent causality in the sense that information propagates along streamlines. This causality is preserved in our discontinuous Galerkin discretization. We can therefore use a simple topological sort of the graph of discrete fluxes to reorder the degrees-of-freedom such that the discretized linear system gets a lower block-triangular form, from which the solution can be computed very efficiently using a single-pass forward block substitution. The accuracy and utility of the resulting transport solver is illustrated through several numerical experiments.     

2.5维起伏地表条件下时间域航空电磁正演模拟

时间域航空电磁作为一种高效地球物理勘探技术特别适合我国地形复杂地区(沙漠、高山、湖泊、沼泽等)资源勘查.然而,这些地区地形起伏较大,对航空电磁响应有严重影响,忽略地形影响会给航空电磁数据解释造成很大误差.到目前为止人们对航空电磁地形效应特征研究十分有限.本文提出了基于非结构化网格的有限元法模拟带地形时间域航空电磁系统响应.该方法与基于结构化网格的有限差分相比能更好地模拟地形.首先通过傅里叶变换将2.5维问题转化成二维问题,利用伽辽金方法对二维问题进行离散.通过使用MUMPS求解器,得到波数域电磁响应.利用反傅里叶变换将波数域电磁响应变换到空间域,并利用正弦变换将其变换到时间域,得到2.5维时间域航空电磁响应.通过将本文的计算结果与半空间模型解析解及其他已发表的结果进行对比,检验了本文算法的精度.最后,我们系统分析了山峰和山谷地形对航空响应的影响特征.本文研究结果对航空电磁地形效应的识别和校正具有指导意义.     

海洋可控源电磁三维非结构矢量有限元数值模拟

本文实现了海洋可控源电磁三维矢量有限元数值模拟.由于采用非结构四面体单元进行三维网格剖分,该方法可以模拟复杂电性异常体和海底地形.一维模型的数值模拟结果表明,电场实、虚部均与解析解吻合得相当好,计算误差基本小于1%.二维模型的计算结果与已有的二维自适应非结构有限元模拟结果吻合很好.带地形模型的数值模拟结果显示,海底地形对电场影响很大,有可能掩盖海底油气藏产生的异常.     

基于非结构化网格的任意复杂2D RMT有限元模拟

射频大地电磁法(RMT)是以潜艇天线发射的射线源等作为场源的一种地球物理勘探方法,目前被广泛应用于近地表工程和环境地球物理勘探.RMT数据解释常采用基于静态假设的大地电磁法(MT)程序,往往会反演出不真实的浅层目标体.为解决这一长期困扰RMT资料解释的问题,本文实现了考虑位移电流的RMT有限元数值模拟.为了处理任意复杂模型,如起伏地形,非结构的三角形网格被用于离散RMT模型.首先通过算例对比,验证了程序的正确性和可靠性.通过Dike模型讨论了空气层厚度对RMT数值解的影响,结果表明当空气层厚度大于1/4波长即可满足精度要求.以山脊模型为例计算了位移电流对RMT响应的影响,表明位移电流的影响会随着山脊高程的增加而增大.最后通过舒家店实际模型进一步验证了位移电流在RMT中的重要性.     

基于电场总场矢量有限元法的接地长导线源三维正演

电磁场数值模拟的背景场/异常场算法是三维正演的有效策略之一,优点为采用解析法计算电磁场背景场代替场源项、克服了场源奇异性,缺点为不适用于发射源布置于起伏地表或背景模型复杂的情形.总场算法是直接对电磁场总场开展数值模拟,其难点是有效加载场源、保证近区与过渡区数值解精度.本文以水平电偶源形式分段加载接地长导线源,并以电场总场Helmholtz方程为矢量有限元法控制方程,实现了基于非结构化四面体网格剖分的接地长导线源频率域电磁法三维正演.通过与均匀全空间中水平电偶源产生的电场解析解对比,验证了本文算法的正确性,并分析了四面体外接圆半径与其最短棱边的最大比值和四面体二面角最小值对数值解精度的影响规律.通过与块状高导体地电模型的积分方程法、有限体积法和基于磁矢量势Helmholtz方程的有限元法数值解对比,进一步验证了本文算法正确性,同时说明了非结构化四面体网格能够更加精细地剖分电性异常体,利于获得精确数值解.     

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.     

Well-balanced high-order centered schemes on unstructured meshes for shallow water equations with fixed and mobile bed

In this paper, we study the numerical approximation of the two-dimensional morphodynamic model governed by the shallow water equations and bed-load transport following a coupled solution strategy. The resulting system of governing equations contains non-conservative products and it is solved simultaneously within each time step. The numerical solution is obtained using a new high-order accurate centered scheme of the finite volume type on unstructured meshes, which is an extension of the one-dimensional PRICE-C scheme recently proposed in Canestrelli et al. (2009) [5]. The resulting first-order accurate centered method is then extended to high order of accuracy in space via a high order WENO reconstruction technique and in time via a local continuous space–time Galerkin predictor method. The scheme is applied to the shallow water equations and the well-balanced properties of the method are investigated. Finally, we apply the new scheme to different test cases with both fixed and movable bed. An attractive future of the proposed method is that it is particularly suitable for engineering applications since it allows practitioners to adopt the most suitable sediment transport formula which better fits the field data.     

Fast data assimilation using a nonlinear Kalman filter and a model surrogate: An application to the Columbia River estuary

A fast and adjoint-free nonlinear data assimilation (DA) system was developed to simulate 3D baroclinic circulation in estuaries, leveraging two recently developed technologies: (1) a nonlinear model surrogate that executes forward simulation three orders of magnitude faster than a forward numerical circulation code and (2) a nonlinear extension to the reduced-dimension Kalman filter that estimates the state of the model surrogate. The noise sources in the Kalman filter were calibrated using empirical cross-validation and accounted for errors in model and model forcing.The DA system was applied to assimilate in situ measurements of water levels, salinities, and temperatures in simulations of the Columbia River estuary. To validate the DA results, we used a combination of cross-validation studies, process-oriented studies, and tests of statistical and dynamical consistency. The validation studies showed that DA improved the representation of several important processes in the estuary, including nonlinear tidal propagation, salinity intrusion, estuarine residual circulation, heat balance, and response of the estuary to coastal winds.