A typhoon-induced storm surge numerical model with GPU acceleration based on an unstructured spherical centroidal Voronoi tessellation grid

Storm surge is often the marine disaster that poses the greatest threat to life and property in coastal areas.Accurate and timely issuance of storm surge warnings to take appropriate countermeasures is an important means to reduce storm surge-related losses.Storm surge numerical models are important for storm surge forecasting.To further improve the performance of the storm surge forecast models,we developed a numerical storm surge forecast model based on an unstructured spherical centroidal Voronoi tessellation(SCVT)grid.The model is based on shallow water equations in vector-invariant form,and is discretized by Arakawa C grid.The SCVT grid can not only better describe the coastline information but also avoid rigid transitions,and it has a better global consistency by generating high-resolution grids in the key areas through transition refinement.In addition,the simulation speed of the model is accelerated by using the openACC-based GPU acceleration technology to meet the timeliness requirements of operational ensemble forecast.It only takes 37 s to simulate a day in the coastal waters of China.The newly developed storm surge model was applied to simulate typhoon-induced storm surges in the coastal waters of China.The hindcast experiments on the selected representative typhoon-induced storm surge processes indicate that the model can reasonably simulate the distribution characteristics of storm surges.The simulated maximum storm surges and their occurrence times are consistent with the observed data at the representative tide gauge stations,and the mean absolute errors are 3.5 cm and 0.6 h respectively,showing high accuracy and application prospects.

A finite volume method for global electromagnetic induction forward modeling on collocated unstructured grids

Global electromagnetic induction provides an efficient way to probe the electrical conductivity in the Earth’s deep interior.Owing to the increasing geomagnetic data especially from high-accuracy geomagnetic satellites,inverting the Earth’s three-dimensional conductivity distribution on a global scale becomes attainable.A key requirement in the global conductivity inversion is to have a forward solver with high-accuracy and efficiency.In this study,a finite volume method for global electromagnetic induction forward modeling is developed based on unstructured grids.Arbitrary polyhedral grids are supported in our algorithms to obtain high geometric adaptability.We employ a cell-centered collocated variable arrangement which allows convenient discretization for complex geometries and straightforward implementation of multigrid technique.To validate the method,we test our code with two synthetic models and compare our finite volume results with an analytical solution and a finite element numerical solution.Good agreements are observed between our solution and other results,indicating acceptable accuracy of the proposed method.

A three-dimensional semi-implicit unstructured grid finite volume ocean model

A new three-dimensional semi-implicit finite-volume ocean model has been developed for simulating the coastal ocean circulation, which is based on the staggered C-unstructured non-orthogonal grid in the hor- izontal direction and z-level grid in the vertical direction. The three-dimensional model is discretized by the semi-implicit finite-volume method, in that the free-surface and the vertical diffusion are semi-implicit, thereby removing stability limitations associated with the surface gravity wave and vertical diffusion terms. The remaining terms in the momentum equations are discretized explicitly by an integral method. The partial cell method is used for resolving topography, which enables the model to better represent irregular topography. The model has been tested against analytical cases for wind and tidal oscillation circulation, and is applied to simulating the tidal flow in the Bohal Sea. The results are in good agreement both with the analytical solutions and measurement results.

Two-dimensional shallow water equations with porosity and their numerical scheme on unstructured grids

In this study, porosity was introduced into two-dimensional shallow water equations to reflect the effects of obstructions, leading to the modification of the expressions for the flux and source terms. An extra porosity source term appears in the momentum equation. The numerical model of the shallow water equations with porosity is presented with the finite volume method on unstructured grids and the modified Roe-type approximate Riemann solver. The source terms of the bed slope and porosity are both decomposed in the characteristic direction so that the numerical scheme can exactly satisfy the conservative property. The present model was tested with a dam break with discontinuous porosity and a flash flood in the Toce River Valley. The results show that the model can simulate the influence of obstructions, and the numerical scheme can maintain the flux balance at the interface with high efficiency and resolution.

Hermite WENO-based limiters for high order discontinuous Galerkin method on unstructured grids

A novel class of weighted essentially nonoscillatory （WENO） schemes based on Hermite polynomi- als, termed as HWENO schemes, is developed and applied as limiters for high order discontinuous Galerkin （DG） method on triangular grids. The developed HWENO methodology utilizes high-order derivative information to keep WENO re- construction stencils in the von Neumann neighborhood. A simple and efficient technique is also proposed to enhance the smoothness of the existing stencils, making higher-order scheme stable and simplifying the reconstruction process at the same time. The resulting HWENO-based limiters are as compact as the underlying DG schemes and therefore easy to implement. Numerical results for a wide range of flow conditions demonstrate that for DG schemes of up to fourth order of accuracy, the designed HWENO limiters can simul- taneously obtain uniform high order accuracy and sharp, es- sentially non-oscillatory shock transition.

A Finite Volume Method with Unstructured Triangular Grids for Numerical Modeling of Tidal Current

The finite volume method （FVM） has many advantages in 2-D shallow water numerical simulation. In this study, the finite volume method is used with unstructured triangular grids to simulate the tidal currents. The Roe scheme is applied in the calculation of the intercell numerical flux, and the MUSCL method is introduced to improve its accuracy. The time integral is a two-step scheme of forecast and revision. For the verification of the present method, the Stoker＇s problem is calculated and the result is compared with the mathematically analytic solutions. The comparison indicates that the method is feasible. A sea area of a port is used as an example to test the method established here. The result shows that the present computational method is satisfactory, and it could be applied to the engineering fields.

Unstructured Grid Immersed Boundary Method for Numerical Simulation of Fluid Structure Interaction

This paper presents an improved unstructured grid immersed boundary method.The advantages of both immersed boundary method and body fitted grids which are generated by unstructured grid technology are used to enhance the computation efficiency of fluid structure interaction in complex domain.The Navier-Stokes equation was discretized spacially with collocated finite volume method and Euler implicit method in time domain.The rigid body motion was simulated by immersed boundary method in which the fluid and rigid body interface interaction was dealt with VOS(volume of solid) method.A new VOS calculation method based on graph was presented in which both immersed boundary points and cross points were collected in arbitrary order to form a graph.The method is verified with flow past oscillating cylinder.

ADAPTIVE LAYERED CARTESIAN CUT CELL METHOD FOR THE UNSTRUCTURED HEXAHEDRAL GRIDS GENERATION

Adaptive layered Cartesian cut cell method is presented to solve the difficulty of the tmstructured hexahedral anisotropic Cartesian grids generation from the complex CAD model. ＂Vertex merging algorithm based on relaxed AVL tree is investigated to construct topological structure for stereo lithography （STL） files, and a topology-based self-adaptive layered slicing algorithm with special features control strategy is brought forward. With the help of convex hull, a new points-in-polygon method is employed to improve the Cartesian cut cell method. By integrating the self-adaptive layered slicing algorithm and the improved Cartesian cut cell method, the adaptive layered Cartesian cut cell method gains the volume data of the complex CAD model in STL file and generates the unstructured hexahedral anisotropic Cartesian grids.

A Coastal Ocean Model of Semi-Implicit Finite Volume Unstructured Grid

A two-dimensional coastal ocean model based on unstructured C-grid is built, in which the momentum equation is discretized on the faces of each cell, and the continuity equation is discretized on the cell. The model is discretized by semi-implicit finite volume method, in that the free surface is semi-implicit and the bottom friction is implicit, thereby removing stability limitations associated with the surface gravity wave and friction. The remaining terms in the momentum equations are discretized explicitly by integral finite volume method and second-order Adams-Bashforth method. Tidal flow in the polar quadrant with known analytic solution is employed to test the proposed model. Finally, the performance of the present model to simulate tidal flow in a geometrically complex domain is examined by simulation of tidal currents in the Pearl River Estuary.

Application of Factor Difference Scheme to Solving Discrete Flow Equations Based on Unstructured Grid

A second-order mixing difference scheme with a limiting factor is deduced with the reconstruction gradient method and applied to discretizing the Navier-Stokes equation in an unstructured grid.The transform of nonorthogonal diffusion items generated by the scheme in discrete equations is provided.The Delaunay triangulation method is improved to generate the unstructured grid.The computing program based on the SIMPLE algorithm in an unstructured grid is compiled and used to solve the discrete equations of two types of incompressible viscous flow.The numerical simulation results of the laminar flow driven by lid in cavity and flow behind a cylinder are compared with the theoretical solution and experimental data respectively.In the former case,a good agreement is achieved in the main velocity and drag coefficient curve.In the latter case,the numerical structure and development of vortex under several Reynolds numbers match well with that of the experiment.It is indicated that the factor difference scheme is of higher accuracy,and feasible to be applied to Navier-Stokes equation.

A fast and reliable overset unstructured grids approach

A cell-centred overset unstructured grids approach is developed.In this approach,the intergrid boundary is initially established based on the wall distance from the cell centre,and is then optimized.To accelerate the intergrid-boundary definition much more,a neighbor-toneighbor donor search algorithm based on advancing-front method is modified with the help of minimum cuboid boxes.To simplify the communications between different grid cell types and to obtain second-order spatial accuracy,a new interpolation method is constructed based on linear reconstruction,which employs only one layer of fringe cells along the intergrid boundary.For unsteady flows with relative motion,the intergrid boundary can be redefined fast and automatically.Several numerical results show that the present dynamic overset unstructured grids approach is accurate and reliable.

Development of A Depth-Integrated Longshore Current Model with Unstructured Grids

A depth-integrated model for simulating wave-induced longshore current was developed with unstructured grids. Effects of surface roller and horizontal mixing under combined waves and currents were incorporated in the numerical model. Recommended values of model coefficients were also proposed based on sensitivity analysis. Field observations and three series of laboratory measurements including two cases conducted on the plane beach and one implemented on the ideal inlet were employed to examine the predictive capability of this model. For the field case and laboratory cases conducted on the plane beach, numerical results were compared favorably with the measured data. For the case with an ideal inlet, simulated circulation pattern is supposed to be reasonable although some deviations between numerical results and measured data still can be detected.

Numerical Simulation of the Three-Dimensional Wave-Induced Currents on Unstructured Grid

By coupling the three-dimensional hydrodynamic model with the wave model, numerical simulations of the three- dimensional wave-induced current are carried out in this study. The wave model is based on the numerical solution of the modified wave action equation and eikonal equation, which can describe the wave refraction and diffraction. The hydrodynamic model is driven by the wave-induced radiation stresses and affected by the wave turbulence. The numerical implementation of the module has used the finite-volume schemes on unstructured grid, which provides great flexibility for modeling the waves and currents in the complex actual nearshore, and ensures the conservation of energy propagation. The applicability of the proposed model is evaluated in calculating the cases of wave set-up, longshore currents, undertow on a sloping beach, rip currents and meandering longshore currents on a tri-cuspate beach. The results indicate that it is necessary to introduce the depth-dependent radiation stresses into the numerical simulation of wave-induced currents, and comparisons show that the present model makes better prediction on the wave procedure as well as both horizontal and vertical structures in the wave-induced current field.

Comparison and Modification: TVD Schemes for Scalar Transport on An Unstructured Grid

In most TVD schemes, the r-factors were proposed according to the cell-centered（CC） finite volume method（FVM） framework for the numerical approximation to the convective term. However, it is questionable whether those r-factors would be appropriate and effective for the vertex-centered（VC） FVM. In the paper, we collected five kinds of r-factor formulae and found out that only three of those, respectively by Bruner（1996）, Darwish and Moukalled（2003） and Cassuli and Zanolli（2005） can be formally extended to a context of the VC FVM. Numerical tests indicate that the TVD schemes and r-factors, after being extended and introduced to a context of the VC FVM, maintained their similar characteristics as in a context of the CC FVM. However, when the gradient-based r-factors and the SUPERBEE scheme were applied simultaneously, non-physical oscillations near the sharp step would appear. In the transient case, the oscillations were weaker in a context of the VC FVM than those in a context of the CC FVM, while the effect was reversed in the steady case. To eliminate disadvantages in the gradient-based r-factor formula, a new modification method by limiting values on the virtual node, namely Фu in the paper, was validated by the tests to effectively dissipate spurious oscillations.

A New Efficient Finite Volume Modeling of Small Amplitude Free Surface Flows with Unstructured Grid

A staggered finite-volume technique for non-hydrostatic, small amplitude free surface flow governed by the incompressible Navier-Stokes equations is presented there is a proper balance between accuracy and computing time. The advection and horizontal diffusion terms in the momentum equation are discretized by an integral interpolation method on the orthogonal unstructured staggered mesh and, while it has the attractive property of being conservative. The pressure-correction algorithm is employed for the non-hydrostatic pressure in order to achieve second-order temporal accuracy. A conservative scalar transport algorithm is also applied to discretize k - c equations in this model. The eddy viscosity is calculated from the k-c turbulent model. The resulting model is mass and momentum conservative. The model is verified by two examples to simulate unsteady small amplitude free surface flows where non-hydrostatic pressures have a considerable effect on the velocity field, and then applied to simulate the tidal flow in the Bohai Sea.

Two Modified QUICK Schemes for Advection-Diffusion Equation of Pollutants on Unstructured Grids

In this paper, two modified QUICK schemes, namely Q-QUICK and UQ-QUICK, for improving the preci-sion of convective flux approximation are verified in advection-diffusion equation of pollutants on unstruc-tured grids. The constructed auxiliary nodes for Q-QUICK/UQ-QUICK are composed of two neighboring nodes plus the next upwind node, the later node is generated from intersection of the line of current neighboring nodes and their corresponding interfaces. 2D unsteady advection-diffusion equation of pollut-ants is conducted for their verifications on unstructured grids. The numerical results show that Q-QUICK and UQ-QUICK have similar computational accuracy to the central difference scheme and similar numerical stability to upwind difference scheme after applying the deferred correction method. In addition, their corre-sponding CPU times are approximately equivalent to those of traditional difference schemes and their abili-ties for adapting high grid deformation are robust.

基于2.5D有限元的高密度电法不同装置勘探效果研究

高密度电法是一种适用性广泛的电阻率勘探方法,拥有多种电极排列装置选择。不同装置由于电极分布方式的差异,在针对不同地质目标和测区环境时往往表现出明显不同的探测能力。为探究各排列装置的特点及其适用情况,推导了2.5D电位的变分问题,采用Delaunay三角化算法实现了非结构化网格剖分,进而实现了有限元正演模拟。结合实践,对常见地质情况进行建模,分别使用温纳α、温纳β、施伦贝谢尔、偶极-偶极4种装置开展正反演对比研究。研究发现:(1)在探测未知区域单个异常体时,温纳β、施伦贝谢尔2种排列的效果更好;(2)在探测相邻较近的多个异常体时,应优先采用具有更高水平分辨率的施伦贝谢尔和偶极-偶极排列;(3)对于低阻破碎带的勘探,温纳β和偶极-偶极排列更为适用;(4)当地层具有较好分层界限时,4种排列均可体现良好的分层效果。因此,高密度电法勘探实践中应综合考虑不同排列装置的特点,根据具体情况选用合适的多种排列方式进行测量,并对采集数据进行综合对比分析,以获得更为准确的解释结果。

非结构化网格下海洋流场的特征提取与种子点选取算法

对于非结构化网格流场数据,现有研究存在不能定位流场中临界点的具体位置、无法对临界点精细分类以及缺乏适用于非结构化网格的种子点选取算法等问题。针对上述问题,基于非结构化网格流场数据,分别在临界点提取和种子点选取方法上进行改进创新。提出非结构化网格中临界点的定位及分类方法,通过庞加莱指数法判断存在临界点的三角网格。构造质心迭代法定位临界点在网格中的准确位置,并设计三角网格内雅克比矩阵的构造方法,将临界点精细分类。基于非结构化网格提出基于最大得分和网格密度的种子点选取算法,先比较相邻格点的标量值大小来计算每个格点的得分,形成“最大得分”标量场,再按照网格密度动态设置阈值,将得分大于阈值的格点选为种子点,接着以种子点为起始点生成流线,生成的流线可以表达出流场的关键特征与全局信息。基于多个海域流场数据的实验结果表明,临界点分类的准确率可达99%以上,证明了临界点提取算法的准确性以及种子点选取算法对提升流场可视化效果的有效性。

起伏地形下基于非结构网格模型降维的重力三维密度反演

复杂起伏地形以及剖分方式对重力反演解释具有重要影响.目前重力密度反演研究主要基于直立长方体模型,这显著降低了对起伏地形和复杂地质体的拟合程度,对重力反演解释易产生较大影响.四面体非结构网格能够更加精细地模拟起伏地形及复杂地质体,为此本文研究了起伏地形条件下基于四面体非结构网格剖分的重力三维密度反演.首先基于Delaunay方法将地下区域剖分为四面体非结构网格,引入垂向导数和相关系数两种方法进行模型降维技术从而减小解的空间,通过添加最小长度约束,深度加权约束,物性范围约束构建目标函数,并采用预条件共轭梯度法求解.为了提高反演效率在计算过程引入OpenMP并行算法.并研究了各项约束以及两种模型降维方法在四面体非结构网格正则化反演中的效果.通过不同深度直立长方体模型以及起伏地形下组合模型试验,基于四面体非结构网格的重力密度反演可以清晰地反映异常体位置.将本文提出的方法应用于美国密苏里州东南部的氧化铁矿床,反演结果与已知岩体具有较好的一致性,进一步证明该方法的正确性和有效性.

复杂地质条件下浅海区电性源瞬变电磁法三维响应特征

与频域电磁法相比,瞬变电磁法可有效区分空气波和海底电磁响应,在浅海油气藏探测中具有良好的应用前景。近海海域地质条件一般较为复杂,普遍具有强切割地形及复杂构造,使电磁场响应特征变得异常复杂,给数据解释工作带来极大困难。本文基于时域有限元法,采用非结构化网格对复杂地质模型进行剖分,通过构建时域有限元方程并结合偶极子离散的长导线源近似技术以及后退欧拉离散技术,实现了复杂地质条件下浅海区电性源瞬变电磁三维正演模拟。在验证算法精度后,通过复杂地质模型的三维正演,分析了不同海水深度对空气波与海底油气藏目标体的影响,在此基础上,进一步分析了不同围岩电阻率以及海底地形对油气藏目标体分辨率的影响,结果表明:在浅海条件下,脉冲响应受空气波影响较大,阶跃响应受空气波影响较小,随着深度增大空气波影响变小,对油气藏的分辨率也降低;围岩电阻率及海底复杂地形对电性源瞬变电磁影响严重。