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1.
Several schemes for scalar advection on unstructured triangular grids are assessed for possible use in ocean modelling applications.
Finite element, finite volume and finite volume–element approaches are evaluated. A series of tests, including a numerical
order of convergence analysis, idealized rotating cone and cylinder experiments, and transport of a tracer through the Stommel
Gyre representation of ocean basin-scale circulation, are carried out. Volume element Eulerian–Lagrangian and third-order
Runge-Kutta discontinuous Galerkin schemes are recommended for use in tracer studies. Taylor–Galerkin and second-order Runge–Kutta
discontinuous Galerkin are found to be robust and accurate second-order schemes. When positivity is required, a fluctuation
redistribution scheme was found to be an easily implemented, accurate, and computationally efficient approach.
Responsible editor: Phil Dyke 相似文献
2.
Richard Comblen Sébastien Blaise Vincent Legat Jean-François Remacle Eric Deleersnijder Jonathan Lambrechts 《Ocean Dynamics》2010,60(6):1395-1414
We describe the time discretization of a three-dimensional baroclinic finite element model for the hydrostatic Boussinesq
equations based upon a discontinuous Galerkin finite element method. On one hand, the time marching algorithm is based on
an efficient mode splitting. To ensure compatibility between the barotropic and baroclinic modes in the splitting algorithm,
we introduce Lagrange multipliers in the discrete formulation. On the other hand, the use of implicit–explicit Runge–Kutta
methods enables us to treat stiff linear operators implicitly, while the rest of the nonlinear dynamics is treated explicitly.
By way of illustration, the time evolution of the flow over a tall isolated seamount on the sphere is simulated. The seamount
height is 90% of the mean sea depth. Vortex shedding and Taylor caps are observed. The simulation compares well with results
published by other authors. 相似文献
3.
Elena Zhebel Sara Minisini Alexey Kononov Wim A. Mulder 《Geophysical Prospecting》2014,62(5):1111-1125
The finite‐difference method on rectangular meshes is widely used for time‐domain modelling of the wave equation. It is relatively easy to implement high‐order spatial discretization schemes and parallelization. Also, the method is computationally efficient. However, the use of finite elements on tetrahedral unstructured meshes is more accurate in complex geometries near sharp interfaces. We compared the standard eighth‐order finite‐difference method to fourth‐order continuous mass‐lumped finite elements in terms of accuracy and computational cost. The results show that, for simple models like a cube with constant density and velocity, the finite‐difference method outperforms the finite‐element method by at least an order of magnitude. Outside the application area of rectangular meshes, i.e., for a model with interior complexity and topography well described by tetrahedra, however, finite‐element methods are about two orders of magnitude faster than finite‐difference methods, for a given accuracy. 相似文献
4.
A wetting and drying method for free-surface problems for the three-dimensional, non-hydrostatic Navier–Stokes equations is proposed. The key idea is to use a horizontally fixed mesh and to apply different boundary conditions on the free-surface in wet and dry zones. In wet areas a combined pressure/free-surface kinematic boundary condition is applied, while in dry areas a positive water level and a no-normal flow boundary condition are enforced. In addition, vertical mesh movement is performed to accurately represent the free-surface motion. Non-physical flow in the remaining thin layer in dry areas is naturally prevented if a Manning–Strickler bottom drag is used. The treatment of the wetting and drying processes applied through the boundary condition yields great flexibility to the discretisation used. Specifically, a fully unstructured mesh with any finite element choice and implicit time discretisation method can be applied. The resulting method is mass conservative, stable and accurate. It is implemented within Fluidity-ICOM [1] and verified against several idealized test cases and a laboratory experiment of the Okushiri tsunami. 相似文献
5.
An unstructured mesh model of the west coast of Britain, covering the same domain and using topography and open boundary forcing
that are identical to a previous validated uniform grid finite difference model of the region, is used to compare the performance
of a finite volume (FV) and a finite element (FE) model of the area in determining tide–surge interaction in the region. Initial
calculations show that although qualitatively both models give comparable tidal solutions in the region, comparison with observations
shows that the FV model tends to under-estimate tidal amplitudes and hence background tidal friction in the eastern Irish
Sea. Storm surge elevations in the eastern Irish Sea due to westerly, northerly and southerly uniform wind stresses computed
with the FV model tend to be slightly higher than those computed with the FE model, due to differences in background tidal
friction. However, both models showed comparable non-linear tide–surge interaction effects for all wind directions, suggesting
that they can reproduce the extensive tide–surge interaction processes that occur in the eastern Irish Sea. Following on from
this model comparison study, the physical processes contributing to surge generation and tide–surge interaction in the region
are examined. Calculations are performed with uniform wind stresses from a range of directions, and the balance of various
terms in the hydrodynamic equations is examined. A detailed comparison of the spatial variability of time series of non-linear
bottom friction and non-linear momentum advection terms at six adjacent nodes at two locations in water depths of 20 and 6 m
showed some spatial variability from one node to another. This suggests that even in the near coastal region, where water
depths are of the order of 6 m and the mesh is fine (of order 0.5 km), there is significant spatial variability in the non-linear
terms. In addition, distributions of maximum bed stress due to tides and wind forcing in nearshore regions show appreciable
spatial variability. This suggests that intensive measurement campaigns and very high-resolution mesh models are required
to validate and reproduce the non-linear processes that occur in these regions and to predict extreme bed stresses that can
give rise to sediment movement. High-resolution meshes will also be required in pollution transport problems. 相似文献
6.
This study is focused on the integration of bare earth lidar (Light Detection and Ranging) data into unstructured (triangular) finite element meshes and the implications on simulating storm surge inundation using a shallow water equations model. A methodology is developed to compute root mean square error (RMSE) and the 95th percentile of vertical elevation errors using four different interpolation methods (linear, inverse distance weighted, natural neighbor, and cell averaging) to resample bare earth lidar and lidar-derived digital elevation models (DEMs) onto unstructured meshes at different resolutions. The results are consolidated into a table of optimal interpolation methods that minimize the vertical elevation error of an unstructured mesh for a given mesh node density. The cell area averaging method performed most accurate when DEM grid cells within 0.25 times the ratio of local element size and DEM cell size were averaged. The methodology is applied to simulate inundation extent and maximum water levels in southern Mississippi due to Hurricane Katrina, which illustrates that local changes in topography such as adjusting element size and interpolation method drastically alter simulated storm surge locally and non-locally. The methods and results presented have utility and implications to any modeling application that uses bare earth lidar. 相似文献
7.
Arjen D. Terwisscha van Scheltinga Paul G. Myers Julie D. Pietrzak 《Ocean Dynamics》2010,60(6):1539-1558
The Canadian Arctic Archipelago (CAA) is a complex area formed by narrow straits and islands in the Arctic. It is an important
pathway for freshwater and sea-ice transport from the Arctic Ocean to the Labrador Sea and ultimately to the Atlantic Ocean.
The narrow straits are often crudely represented in coupled sea-ice–ocean models, leading to a misrepresentation of transports
through these straits. Unstructured meshes are an alternative in modelling this complex region, since they are able to capture
the complex geometry of the CAA. This provides higher resolution in the flow field and allows for more accurate transports
(but not necessarily better modelling). In this paper, a finite element sea-ice model of the Arctic region is described and
used to estimate the sea-ice fluxes through the CAA. The model is a dynamic–thermodynamic sea-ice model with elastic–viscous–plastic
rheology and is coupled to a slab ocean, where the temperature and salinity are restored to climatology, with no velocities
and surface elevation. The model is spun-up from 1973 to 1978 with NCEP/NARR reanalysis data. From 1979 to 2007, the model
is forced by NCEP/DoE reanalysis data. The large scale sea-ice characteristics show good agreement with observations. The
total sea-ice area agrees very well with observations and shows a sensitivity to the Arctic oscillation (AO). For 1998–2002,
we find estimates for the sea-ice volume and area fluxes through Admunsen Gulf, McClure Strait and the Queen Elizabeth Islands
that compare well with observation and are slightly better than estimates from other models. For Nares Strait, we find that
the fluxes are much lower than observed, due to the missing effect of topographic steering on the atmospheric forcing fields.
The 1979–2007 fluxes show large seasonal and interannual variability driven primarily by variability in the ice velocity field
and a sensitivity to the AO and other large-scale atmospheric variability, which suggests that accurate atmospheric forcing
might be crucial to modelling the CAA. 相似文献
8.
Vir&#; Axelle Xiang Jiansheng Milthaler Frank Farrell Patrick Emmet Piggott Matthew David Latham John-Paul Pavlidis Dimitrios Pain Christopher Charles 《Ocean Dynamics》2012,62(10):1487-1501
Fluid–structure interactions are modelled by coupling the finite element fluid/ocean model ‘Fluidity-ICOM’ with a combined finite–discrete element solid model ‘Y3D’. Because separate meshes are used for the fluids and solids, the present method is flexible in terms of discretisation schemes used for each material. Also, it can tackle multiple solids impacting on one another, without having ill-posed problems in the resolution of the fluid’s equations. Importantly, the proposed approach ensures that Newton’s third law is satisfied at the discrete level. This is done by first computing the action–reaction force on a supermesh, i.e. a function superspace of the fluid and solid meshes, and then projecting it to both meshes to use it as a source term in the fluid and solid equations. This paper demonstrates the properties of spatial conservation and accuracy of the method for a sphere immersed in a fluid, with prescribed fluid and solid velocities. While spatial conservation is shown to be independent of the mesh resolutions, accuracy requires fine resolutions in both fluid and solid meshes. It is further highlighted that unstructured meshes adapted to the solid concentration field reduce the numerical errors, in comparison with uniformly structured meshes with the same number of elements. The method is verified on flow past a falling sphere. Its potential for ocean applications is further shown through the simulation of vortex-induced vibrations of two cylinders and the flow past two flexible fibres.
相似文献9.
本文基于非结构网格实现了海洋可控源电磁法三维有限元正演模拟.该算法采用完全非结构网格剖分,可以模拟任意起伏地形和复杂地电模型.为了避免场源的奇异性,采用一次场/二次场分解算法,一次场由基于Schelkunoff势函数的一维解析公式得到.为了提高算法的精度和效率,采用对测点附近单元和异常体区域进行体积约束加密的方法,实现了非结构网格的局部加密.一、二维模型计算和分析表明,本文采用的局部加密方法能够明显地改善算法的精度,最大相对误差基本在1%以内.对三维模型计算及对比分析,说明了该算法对三维可控源电磁正演的实用性.复杂海底地形模型的正演模拟表明,海底地形对电磁场的影响很大,在进行海洋可控源电磁资料解释时,地形的影响有必要考虑在内. 相似文献
10.
Axelle Viré Jiansheng Xiang Frank Milthaler Patrick Emmet Farrell Matthew David Piggott John-Paul Latham Dimitrios Pavlidis Christopher Charles Pain 《Ocean Dynamics》2012,62(10-12):1487-1501
Fluid–structure interactions are modelled by coupling the finite element fluid/ocean model ‘Fluidity-ICOM’ with a combined finite–discrete element solid model ‘Y3D’. Because separate meshes are used for the fluids and solids, the present method is flexible in terms of discretisation schemes used for each material. Also, it can tackle multiple solids impacting on one another, without having ill-posed problems in the resolution of the fluid’s equations. Importantly, the proposed approach ensures that Newton’s third law is satisfied at the discrete level. This is done by first computing the action–reaction force on a supermesh, i.e. a function superspace of the fluid and solid meshes, and then projecting it to both meshes to use it as a source term in the fluid and solid equations. This paper demonstrates the properties of spatial conservation and accuracy of the method for a sphere immersed in a fluid, with prescribed fluid and solid velocities. While spatial conservation is shown to be independent of the mesh resolutions, accuracy requires fine resolutions in both fluid and solid meshes. It is further highlighted that unstructured meshes adapted to the solid concentration field reduce the numerical errors, in comparison with uniformly structured meshes with the same number of elements. The method is verified on flow past a falling sphere. Its potential for ocean applications is further shown through the simulation of vortex-induced vibrations of two cylinders and the flow past two flexible fibres. 相似文献
11.
波动问题有限元离散后会引起数值误差, 数值频散的本质就是数值误差传播引起的非物理解. 数值频散不仅没有实际意义, 而且还会影响对真实波动现象的认识. 为厘清有限元三角网格中波动数值频散的影响因素, 本文推导了集中质量矩阵和一致质量矩阵的频散函数, 同时给出了组合质量矩阵的频散函数, 并对不同质量矩阵的数值频散进行了对比研究. 理论分析和数值计算结果表明: 有限元三角网格中波动的数值频散受网格布局、 波传播方向、 单元网格纵横比以及质量矩阵的影响; 一致质量矩阵的数值频散比集中质量矩阵更易受到波传播方向的影响; 不合理的三角网格单元会对数值相速度(数值频散)产生不良影响; 正三角网格中波动的数值频散几乎不受波传播方向的影响; 一致质量矩阵与集中质量矩阵的线性组合能够有效地压制数值频散. 相似文献
12.
The problem of flow separation around islands is investigated using a dynamically adaptive finite element model to allow for
resolution of the shear layers that form in the advent of separation. The changes in secondary circulation and vertical motion
that occur in both attached and separated flows are documented, as is the degree of closure of the wake eddies. In the numerical
experiments presented, the strongest motion always takes place at the sides of the idealised island, where flow curvature
and shear act together to induce ascent. In contrast, it is the slower motion within the wake eddies that allow streamlines
to extend from the bottom to the surface. We find no evidence for closure of the wake eddies. Rather, all of our separated
experiments show that streamlines that pass through the eddies originate outside of the shear layers and frictional boundary
layers on the upstream side of the idealised island. The numerical experiments demonstrate the potential for dynamically adaptive,
unstructured meshes to resolve the separated shear layers that occur downstream of the idealised island, as well as the narrow
boundary layers that form on the island itself. 相似文献
13.
地表起伏地形在野外矿产资源勘察中不可避免,其对直流电阻率法勘探影响巨大.近年来,电阻率三维正演取得诸多进展,特别是应用非结构网格我们能够进行任意复杂地形和几何模型的电阻率三维数值模拟,但面向实际应用的起伏地形下电阻率三维反演依然困难.本文基于非结构化四面体网格,并考虑到应用GPS/GNSS时,区域地球物理调查中可非规则布设测网的实际特点,实现了任意地形(平坦或起伏)条件下、任意布设的偶极-偶极视电阻率数据的不完全Gauss-Newton三维反演.合成数据的反演结果表明了方法的有效性,可应用于复杂野外环境下的三维电法勘探. 相似文献
14.
In this paper, we present the development and application of a two-dimensional, automatic unstructured mesh generator for shallow water models called Admesh. Starting with only target minimum and maximum element sizes and points defining the boundary and bathymetry/ topography of the domain, the goal of the mesh generator is to automatically produce a high-quality mesh from this minimal set of input. From the geometry provided, properties such as local features, curvature of the boundary, bathymetric/topographic gradients, and approximate flow characteristics can be extracted, which are then used to determine local element sizes. The result is a high-quality mesh, with the correct amount of refinement where it is needed to resolve all the geometry and flow characteristics of the domain. Techniques incorporated include the use of the so-called signed distance function, which is used to determine critical geometric properties, the approximation of piecewise linear coastline data by smooth cubic splines, a so-called mesh function used to determine element sizes and control the size ratio of neighboring elements, and a spring-based force equilibrium approach used to improve the element quality of an initial mesh obtained from a simple Delaunay triangulation. Several meshes of shallow water domains created by the new mesh generator are presented.
相似文献15.
In this paper, we present the development and application of a two-dimensional, automatic unstructured mesh generator for shallow water models called Admesh. Starting with only target minimum and maximum element sizes and points defining the boundary and bathymetry/ topography of the domain, the goal of the mesh generator is to automatically produce a high-quality mesh from this minimal set of input. From the geometry provided, properties such as local features, curvature of the boundary, bathymetric/topographic gradients, and approximate flow characteristics can be extracted, which are then used to determine local element sizes. The result is a high-quality mesh, with the correct amount of refinement where it is needed to resolve all the geometry and flow characteristics of the domain. Techniques incorporated include the use of the so-called signed distance function, which is used to determine critical geometric properties, the approximation of piecewise linear coastline data by smooth cubic splines, a so-called mesh function used to determine element sizes and control the size ratio of neighboring elements, and a spring-based force equilibrium approach used to improve the element quality of an initial mesh obtained from a simple Delaunay triangulation. Several meshes of shallow water domains created by the new mesh generator are presented. 相似文献
16.
Sébastien Blaise Benjamin de Brye Anouk de Brauwere Eric Deleersnijder Eric J. M. Delhez Richard Comblen 《Ocean Dynamics》2010,60(3):535-554
At high Peclet number, the residence time exhibits a boundary layer adjacent to incoming open boundaries. In a Eulerian model,
not resolving this boundary layer can generate spurious oscillations that can propagate into the area of interest. However,
resolving this boundary layer would require an unacceptably high spatial resolution. Therefore, alternative methods are needed
in which no grid refinement is required to capture the key aspects of the physics of the residence time boundary layer. An
extended finite element method representation and a boundary layer parameterisation are presented and tested herein. It is
also explained how to preserve local consistency in reversed time simulations so as to avoid the generation of spurious residence
time extrema. Finally, the boundary layer parameterisation is applied to the computation of the residence time in the Scheldt
Estuary (Belgium/The Netherlands). This timescale is simulated by means of a depth-integrated, finite element, unstructured
mesh model, with a high space–time resolution. It is seen that the residence time temporal variations are mainly affected
by the semi-diurnal tides. However, the spring–neap variability also impacts the residence time, particularly in the sandbank
and shallow areas. Seasonal variability is also observed, which is induced by the fluctuations over the year of the upstream
flows. In general, the residence time is an increasing function of the distance to the mouth of the estuary. However, smaller-scale
fluctuations are also present: they are caused by local bathymetric features and their impact on the hydrodynamics. 相似文献
17.
有限元网格中波动的频散与稳定性的一种改进方法 总被引：1，自引：0，他引：1
本文采用含有频率的高阶位移函数,由二维波动方程导出了波在有限元网格中传播的频散关系,利用这一关系给出了波动的稳定条件。理论分析和数值计算结果表明,文中的有限元方法明显地改善了有限元网格中波动的频散性和稳定性。 相似文献
18.
本文对声波与弹性波方程进行有限元法离散,构造有限元法频散关系的一般特征值问题,分析了时间离散格式为中心差分的三角网格有限元法声波与弹性波模拟的频散特性. 比较了三种质量矩阵即分布式质量矩阵、集中质量矩阵和混合质量矩阵对有限元法频散的影响;选取四种典型三角网格,分析了混合质量矩阵有限元（MFEM）频散的方向各向异性;数值频散、方向各向异性随插值阶数的增加逐渐减弱,当空间为三阶插值时,频散主要表现为随采样率的变化而几乎无明显方向各向异性, 其频散幅值也较小. 控制其他影响因素不变的情况下,研究了不同波速比介质中弹性波的数值频散. 最后给出了三角网格MFEM的数值耗散性. 相似文献
19.
The finite element method is widely employed in numerical analysis of seismic liquefaction at present. However, due to the mesh distortion in strong dynamic action, the results are generally inaccurate and can even stop the calculation. Therefore, an adaptive mesh refinement (AMR) scheme is introduced to improve the numerical results based on a finite element and finite difference coupled dynamic method (FEM–FDM). The changing law about the errors due to the linear and the bilinear recovered fields of coarse meshes, AMR meshes and fine meshes is discussed. The seismic response on soil is compared between different AMR meshes. The AMR strategy can better simulate seismic liquefaction and offer more accurate results than the normal finite element simulation. 相似文献
20.
A variable mesh finite element model of the Irish and Celtic Sea regions with/without the inclusion of the Mersey estuary is used to examine the influence of grid resolution and the Mersey upon the higher harmonics of the tide in the region. Comparisons are made with observations and published results from finite difference models of the area. Although including a high resolution representation of the Mersey had little effect upon computed tides in the western Irish Sea it had a significant effect upon tidal currents in the eastern Irish Sea. In addition the higher harmonics of the M2 tide in near-shore regions of the eastern Irish Sea particularly the Solway and Mersey estuary together with Morecambe Bay showed significant small scale variability. The Mersey was used to test the sensitivity to including estuaries because high resolution accurate topography was available. The results presented here suggest that comparable detailed topographic data sets are required in all estuaries and near-shore regions. In addition comparisons clearly show the need for an unstructured grid model of the region that can include all the estuaries. Such an unstructured grid solution was developed here within a finite element approach, although other methods in particular the finite volume, or coordinate transformations/curvilinear grids and nesting could be applied. 相似文献