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Numerical Modeling of the Hyperbolic Mild-Slope Equation in Curvilinear Coordinates 被引量:4
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作者 佟飞飞 沈永明 +1 位作者 唐军 崔雷 《China Ocean Engineering》 SCIE EI 2010年第4期585-596,共12页
The mild-slope equation is familiar to coastal engineers as it can effectively describe wave propagation in nearshore regions. However, its computational method in Cartesian coordinates often renders the model inaccur... The mild-slope equation is familiar to coastal engineers as it can effectively describe wave propagation in nearshore regions. However, its computational method in Cartesian coordinates often renders the model inaccurate in areas with irregular shorelines, such as estuaries and harbors. Based on the hyperbolic mild-slope equation in Cartesian coordinates, the numerical model in orthogonal curvilinear coordinates is developed. The transformed model is discretized by the finite difference method and solved by the ADI method with space-staggered grids. The numerical predictions in curvilinear co- ordinates show good agreemenl with the data obtained in three typical physical expedments, which demonstrates that the present model can be used to simulate wave propagation, for normal incidence and oblique incidence, in domains with complicated topography and boundary conditions. 展开更多
关键词 mild-slope equation curvilinear coordinates water propagation numerical modeling
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Numerical Simulation of Wave-Induced Currents Combined with Parabolic Mild-Slope Equation in Curvilinear Coordinates 被引量:2
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作者 崔雷 佟飞飞 石峰 《China Ocean Engineering》 SCIE EI 2011年第3期457-468,共12页
Researches on breaking-induced currents by waves are summarized firstly in this paper. Then, a combined numerical model in orthogonal curvilinear coordinates is presented to simulate wave-induced current in areas with... Researches on breaking-induced currents by waves are summarized firstly in this paper. Then, a combined numerical model in orthogonal curvilinear coordinates is presented to simulate wave-induced current in areas with curved boundary or irregular coastline. The proposed wave-induced current model includes a nearshore current module established through orthogonal curvilinear transformation form of shallow water equations and a wave module based on the curvilinear parabolic approximation wave equation. The wave module actually serves as the driving force to provide the current module with required radiation stresses. The Crank-Nicolson finite difference scheme and the alternating directions implicit method are used to solve the wave and current module, respectively. The established surf zone currents model is validated by two numerical experiments about longshore currents and rip currents in basins with rip channel and breakwater. The numerical results are compared with the measured data and published numerical results. 展开更多
关键词 wave-induced current curvilinear coordinates mild-slope equation shallow water equations radiationstress
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3D Numerical Simulation of Overbank Flow in Non-Orthogonal Curvilinear Coordinates 被引量:2
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作者 张明亮 沈永明 吴修广 《China Ocean Engineering》 SCIE EI 2005年第3期395-407,共13页
The velocity field in meandering compound channels with overhank flow is highly three dimensional. To date, its features have been investigated experimentally and little research has been undertaken to investigate the... The velocity field in meandering compound channels with overhank flow is highly three dimensional. To date, its features have been investigated experimentally and little research has been undertaken to investigate the feasibility of reproducing these velocity fields with computer models. If computer modeling were to prove successful in this context, it could become a useful prediction technique and research tool to enhance our understanding of natural river dynamics. A 3-D k-E turbulence hydrodynamic model in curvilinear coordinates is established to simulate the overhank flow. The bodyfitted coordinate is adopted in the horizontal plane, the part grid is adopted in the vertical direction, and the wall-function method is employed to simulate the bed resistance. The model is applied to the simulation of the meandering channel with straight flood plain banks, and the main velocities and secondary velocities for both the longitudinal and cross sections are presented. Comparison and analysis show that the results of simulation are fit to reflect the results of experiment. These results show the application value of the model to 3D overhank flow. 展开更多
关键词 non-orthogonal curvilinear coordinates overbank flow wall-function method k-ε turbulence model
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A Numerical Model of Nonlinear Wave Propagation in Curvilinear Coordinates 被引量:1
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作者 周华伟 张洪生 《China Ocean Engineering》 SCIE EI 2010年第4期597-610,共14页
For the simulation of the nonlinear wave propagation in coastal areas with complex boundaries, a numerical model is developed in curvilinear coordinates. In the model, the Boussinesq-type equations including the dissi... For the simulation of the nonlinear wave propagation in coastal areas with complex boundaries, a numerical model is developed in curvilinear coordinates. In the model, the Boussinesq-type equations including the dissipation terms are em- ployed as the governing equations. In the present model, the dependent variables of the transformed equations are the free surface elevation and the utility velocity variables, instead of the usual primitive velocity variables. The introduction of utility velocity variables which are the products of the contravariant components of the velocity vector and the Jacobi ma- trix can make the transformed equations relatively concise, the treatment of lateral boundary conditions easier and the de- velopment of the program simpler. The predictor-corrector method and five-point finite-difference scheme are employed to discretize the time derivatives and the spatial ones, respectively. The numerical model is tested for three cases. It is found that the numerical results are in good agreement with the analytical results and experimental data. 展开更多
关键词 numerictd model generalized curvilinear coordinates Boussinesq equations corrtravariant velocity
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Numerical model of flow and pollutant transportation in non-orthogonal curvilinear coordinates
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作者 WUXiu-guang SHENYong-ming +1 位作者 ZHENGYong-hong YANGZhi-feng 《Journal of Environmental Sciences》 SCIE EI CAS CSCD 2004年第2期293-296,共4页
The planar 2D k-ε double equations' turbulence model was adopted and transformed into non-orthogonal curvilinear coordinates. The concentration convection-diffusion was introduced to planar 2D SIMPLEC algorithm o... The planar 2D k-ε double equations' turbulence model was adopted and transformed into non-orthogonal curvilinear coordinates. The concentration convection-diffusion was introduced to planar 2D SIMPLEC algorithm of flow in non-orthogonal curvilinear coordinates. The numerical model of pollutant transportation in non-orthogonal curvilinear coordinates was constructed. The model was applied to simulate the flow and pollutant concentration fields. In the testing concentration field, two optimal operations of contamination discharging both along bank and in the centerline at the first bend of the meandering channel were adopted. Comparison with available data showed the model developed was successful, was valuable to engineering application. 展开更多
关键词 curvilinear coordinates diffusion-transportation SIMPLEC algorithm concentration fields meandering channel
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Expression of strain tensor in orthogonal curvilinear coordinates
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作者 Xuyan Liu Yingfeng Ji Quanqiang Liang 《Geodesy and Geodynamics》 2010年第1期48-56,共9页
Based on an analysis of connotation and extension of the concept of the orthogonal curvilinear coordinates, we have deduced a platform of strain tensor expression of Cartesian coordinates, which turns out to be a func... Based on an analysis of connotation and extension of the concept of the orthogonal curvilinear coordinates, we have deduced a platform of strain tensor expression of Cartesian coordinates, which turns out to be a function of Lame coefficient and unit vector. By using transform matrix between Cartesian coordinates and orthogonal eurvilinear coordinates, we have deduced a mathematical expression for correcting displacement vector differential in orthogonal curvilinear coordinates, and given a general expression of strain tensor in orthogonal curvilinear coordinates. 展开更多
关键词 Orthogonal curvilinear coordinates OCC Cartesian coordinates strain tensor transformation matrix universal expression
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Electrodynamics in Curvilinear Coordinates and the Equation of a Geodesic Line
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作者 Anatoly V. Parfyonov 《Journal of Modern Physics》 CAS 2022年第11期1382-1402,共21页
The creation of the theory of relativity, which discovered the equivalence of mass and energy, showed that the concept of a point charge, used in the formulation of Coulomb’s law, one of the basic laws of classical e... The creation of the theory of relativity, which discovered the equivalence of mass and energy, showed that the concept of a point charge, used in the formulation of Coulomb’s law, one of the basic laws of classical electrodynamics, contradicts the famous formula establishing the equivalence of mass and energy. But the discovery of quarks makes it possible to present classical electrodynamics in a form free from the indicated contradiction. In the article, having considered the electromagnetic field in a curvilinear coordinate system, a theory has been created that expands our understanding of the electromagnetic field, the nature of quarks, the nature of strong interaction, and the connection between strong interaction and electromagnetic interaction. This theory is based on the principle of equivalence of an electromagnetic field to a free material particle formulated in the article and the law of formation of elementary particles from an electromagnetic field that follows from it. 展开更多
关键词 ELECTRODYNAMICS Electromagnetic Field curvilinear coordinates QUARKS Strong Interaction Equation of a Geodesic Line
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NUMERICAL SIMULATION OF 2D HORIZONTAL COOLING WATER DISCHARGE IN GENERALIZED CURVILINEAR COORDINATE 被引量:11
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作者 XIE Zuo-tao ZHANG Xiao-feng TAN Guang-ming YANG Fang-li 《Journal of Hydrodynamics》 SCIE EI CSCD 2006年第1期91-96,共6页
2D horizontal model is one of the major mathematical methods for the research on cooling water discharge from the power plant. In this paper, the shallow water equations are transformed under the generalized curviline... 2D horizontal model is one of the major mathematical methods for the research on cooling water discharge from the power plant. In this paper, the shallow water equations are transformed under the generalized curvilinear coordinate system and the elliptic differential equations are used to generate curvilinear grids, so a model in generalized curviline ar coordinate is presented to simulate 2D horizontal cooling water, Governing equations of the model are discretized by finite volume method, and non-staggered grids and SIMPLE algorithm are introduced to simplify the program during the discretization. This model is used to simulate the movement of cooling water in a simplified meandering channel and a natural channel, calculating results indicate this model can correctly reflect the movement rules of cooling water, which verifies the model can be applied in engineering practice. 展开更多
关键词 cooling water generalized curvilinear coordinate non-staggered grids numerical simulation SIMPLE algorithm
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MATHEMATICAL MODEL FOR 2-D TIDAL FLOW AND WATER QUALITY WITH ORTHOGONAL CURVILINEAR COORDINATES 被引量:6
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作者 LiuYu-ling WeiWen-li ShenYong-ming 《Journal of Hydrodynamics》 SCIE EI CSCD 2003年第5期103-108,共6页
This paper presents a numerical method for simulating the 2-D tidal flow andwater quality with the orthogonal curvilinear coordinates. In order to overcome the computationaldifficulties in natural rivers, such as the ... This paper presents a numerical method for simulating the 2-D tidal flow andwater quality with the orthogonal curvilinear coordinates. In order to overcome the computationaldifficulties in natural rivers, such as the complicated boundary figures, the great disparitybetween length and width of computational domain, etc. , orthogonal boundary-filled grid was used.The irregular domain in physical plane was transformed into a rectangular domain in a transformedplane, and the depth-averaged momentum equations and mass equation were given and discretized basedon the alternating direction implicit finite difference scheme in curvilinear coordinates. Theapplication of the presented method was illustrated by an example of analyzing the Yangtze River inthe vicinity of Nanjing city. A fair agreement between the measured data and computed resultsdemonstrates the validity of the developed method. 展开更多
关键词 orthogonal curvilinear coordinate boundary-fitted grid numerical simulationflow water quality tidal river
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NUMERICAL SIMULATION OF 2-D TIDAL FLOW AND WATER QUALITY UNDER THE CURVILINEAR COORDINATES 被引量:3
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作者 Wang Jia-heDept. of Hydro-power Engineering, Hohai Univ. , Nanjing 210098, P. R. ChinaWang ChaoDept. of Environmental Engineering, Hohai Univ. , Nanjing 210098, P. R. China 《Journal of Hydrodynamics》 SCIE EI CSCD 1994年第3期78-84,共7页
This paper presents a numerical method to simulate the 2-D tidal flow and water quality under the curvilinear coordinates. In order to overcome the computational difficulties in natural rivers, such as the complicated... This paper presents a numerical method to simulate the 2-D tidal flow and water quality under the curvilinear coordinates. In order to overcome the computational difficulties in natural rivers, such as the complicated boundary figures, the great disparity between length and width of computational domain, etc. , boundary-fitted grid is used, the irregular domain in physical plane is transformed into a rectangular domain in transformed plane, and the depth-averaged momentum equations and mass equation are rewritten and discretized based on the finite volume techniques in curvilinear coordinates. Practical application of the method is illustrated by an example for the Dachangzhen Section of the Yangtze River. A fair agreement between the values measured and computed demonstrates the validity of the method developed. 展开更多
关键词 curvilinear coordinate boundary-fitted grid numerical simulation FLOW water quality tidal river.
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Vorticity vector-potential method based on time-dependent curvilinear coordinates for two-dimensional rotating flows in closed configurations 被引量:3
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作者 Yuan Fu Da-peng Zhang Xi-lin Xie 《Journal of Hydrodynamics》 SCIE EI CSCD 2018年第2期218-234,共17页
In this study, a vorticity vector-potential method for two-dimensional viscous incompressible rotating driven flows is developed in the time-dependent curvilinear coordinates. The method is applicable in both inertial... In this study, a vorticity vector-potential method for two-dimensional viscous incompressible rotating driven flows is developed in the time-dependent curvilinear coordinates. The method is applicable in both inertial and non-inertial frames of reference with the advantage of a fixed and regular calculation domain. The numerical method is applied to triangle and curved triangle configurations in constant and varying rotational angular velocity cases respectively. The evolutions of flow field are studied. The geostrophic effect, unsteady effect and curvature effect on the evolutions are discussed. 展开更多
关键词 Rotating driven flow time-dependent curvilinear coordinate geostrophic effect unsteady effect curvature effect
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WATER WAVE SIMULATION IN CURVILINEAR COORDINATES USING A TIME-DEPENDENT MILD SLOPE EQUATION 被引量:2
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作者 TONG Fei-fei SHEN Yong-ming +1 位作者 TANG Jun CUI Lei 《Journal of Hydrodynamics》 SCIE EI CSCD 2010年第6期796-803,共8页
The purpose of this article is to model the detailed progress of wave propagation in curvilinear coordinates with an effective time-dependent mild slope equation. This was achieved in the following approach, firstly d... The purpose of this article is to model the detailed progress of wave propagation in curvilinear coordinates with an effective time-dependent mild slope equation. This was achieved in the following approach, firstly deriving the numerical model of the equation, i.e., Copeland's hyperbolic mild-slope equation, in orthogonal curvilinear coordinates based on principal of coordinate transformation, and then finding the numerical solution of the transformed model by use of the Alternative Directions Implicit (ADI) method with a space-staggered grid. To test the curvilinear model, two cases of a channel with varying cross section and a semi-circular channel were studied with corresponding analytical solutions. The model was further investigated through a numerical simulation in Ponce de Leon Inlet, USA. Good agreement is reached and therefore, the use of the present model is valid to calculate the progress of wave propagation in areas with curved shorelines, nearshore breakwaters and other complicated geometries. 展开更多
关键词 curvilinear coordinates mild slope equation water wave ANALYTICAL numerical modeling
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SPACE-TIME CONSERVATION SCHEME IN NONORTHOGONAL CURVILINEAR COORDINATES 被引量:1
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作者 刘海涛 徐建中 黄修乾 《Chinese Journal of Aeronautics》 SCIE EI CSCD 1998年第3期6-17,共12页
A scheme of space time conservation (STC) based on the method of space time conservation element and solution element (CE/SE) is represented in a nonorthogonal curvilinear coordinate system. The corresponding initia... A scheme of space time conservation (STC) based on the method of space time conservation element and solution element (CE/SE) is represented in a nonorthogonal curvilinear coordinate system. The corresponding initial and boundary conditions are discussed. It is seen that in the nonorthogonal coordinates the scheme maintains the advantages of the STC method, and is noted for its simple structure, clear physical meaning, rapid calculation and high accuracy. It is easy to extend to the multidimensional flow. The numerical results for a 2D Euler equation show good agreement with those from other computational methods and the experiment. 展开更多
关键词 computational method nonorthogonal curvilinear coordinates
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Lattice Boltzmann model for shallow water in curvilinear coordinate grid
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作者 赵庄明 黄平 李少钿 《Journal of Hydrodynamics》 SCIE EI CSCD 2017年第2期251-260,共10页
In this study, a multi-relaxation time lattice Boltzmann model for shallow water in a curvilinear coordinate grid is developed using the generalized form of the interpolation supplemented lattice Boltzmann method. The... In this study, a multi-relaxation time lattice Boltzmann model for shallow water in a curvilinear coordinate grid is developed using the generalized form of the interpolation supplemented lattice Boltzmann method. The Taylor-Colette flow tests show that the proposed model enjoys a second order accuracy in space. The proposed model is applied to three types of meandering channels with 180°, 90°and 60° consecutive bends. The numerical results demonstrate that the simulated results agree well with previous computational and experimental data. In addition, the model can achieve the acceptable accuracy in terms of the water depth and the depth-averaged velocities for shallow water flows in curved and meandering channels over a wide range of bend angles. 展开更多
关键词 curvilinear coordinate lattice Boltzmann method meandering flow multi-relaxation-time model shallow water
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Accelerating CFD simulation with high order finite difference method on curvilinear coordinates for modern GPU clusters
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作者 Chuang-Chao Ye Peng-Jun-Yi Zhang +2 位作者 Zhen-Hua Wan Rui Yan De-Jun Sun 《Advances in Aerodynamics》 2022年第1期115-146,共32页
A high fidelity flow simulation for complex geometries for high Reynolds number(Re)flow is still very challenging,requiring a more powerful HPC system.However,the development of HPC with traditional CPU architecture s... A high fidelity flow simulation for complex geometries for high Reynolds number(Re)flow is still very challenging,requiring a more powerful HPC system.However,the development of HPC with traditional CPU architecture suffers bottlenecks due to its high power consumption and technical difficulties.Heterogeneous architecture computation is raised to be a promising solution to the challenges of HPC development.GPU accelerating technology has been utilized in low order scheme CFD solvers on the structured grid and high order scheme solvers on unstructured meshes.The high-order finite difference methods on structured grids possess many advantages,e.g.,high efficiency,robustness,and low storage.However,the strong dependence among points for a high-order finite difference scheme still limits its application on the GPU platform.In the present work,we propose a set of hardware-aware technology to optimize data transfer efficiency between CPU and GPU,as well as communication efficiency among GPUs.An in-house multi-block structured CFD solver with high order finite difference methods on curvilinear coordinates is ported onto the GPU platform and obtains satisfying performance with a speedup maximum of around 2000x over a single CPU core.This work provides an efficient solution to apply GPU computing in CFD simulation with specific high order finite difference methods on current GPU heterogeneous computers.The test shows that significant accelerating effects can be achieved for different GPUs. 展开更多
关键词 Hardware-aware High order Finite difference methods curvilinear coordinates GPU
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NUMERICAL SIMULATION OF HIGH TURBULENT FREE SURFACE FLOW UNDER THE CURVILINEAR COORDINATES
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作者 Xu Wei-xin, Jin Zhong-qingWater Power Department of Hohai University, Nanjing 210098. P. R. ChinaWang Da-yunHarbin Engineering University, Harbin 150001, P. R.China 《Journal of Hydrodynamics》 SCIE EI CSCD 1997年第3期1-8,共8页
This paper presents a new numerical method to simulate the high velocity turbulent flow with free surface by solving two-dimensional incompressible unsteady Navier-Stokes Eqs. , together with the k-ε turbulence model... This paper presents a new numerical method to simulate the high velocity turbulent flow with free surface by solving two-dimensional incompressible unsteady Navier-Stokes Eqs. , together with the k-ε turbulence model. In order to treat the non-rectangular boundary (or curvilinear boundary), orthogonal boundary-fitted grid is used and the Navier-Stokes Eqs. and k-ε turbulence model are rewritten and discreted in orthogonal curvilinear coordinates. Meanwhile, gas-liquid two-field model theory is introduced to treat the free-surface problem. 展开更多
关键词 k-εturbulence model curvilinear coordinates unsteady simulation nonlinear free surface motion
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Staggered Calculation of Turbulent Flows Over a 3D Bluff Body Using Curvilinear Nonorthogonal Coordinates
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作者 Zhao Haiheng Zhang Xiaogang(School of Medchanical Engineering, Southwest Jiaotong Univrsity Chengdu 6 1 003 1, China) 《Journal of Modern Transportation》 1995年第1期93-100,共8页
A finite difference method is developed to predict turbulent flows over 3D bluffbodies. The K-ε turbulence model with Launder and Spalding's wall treatment isemployed. The solution alsorithm is based on a body fi... A finite difference method is developed to predict turbulent flows over 3D bluffbodies. The K-ε turbulence model with Launder and Spalding's wall treatment isemployed. The solution alsorithm is based on a body fitted nonorthogonalcurvilinear eourdinate system and a stagsered grid arrangement. The covariantvelocity components are chosen as dependent variables. Convective fluxes aredescribed by the Power haw Scheme. The grids are generated with an ellipticgrid generator using control functions. Results obtained are compared withexporiment measurements and other calculations. 展开更多
关键词 turbulent flows nonorthogonal curvilinear coordinates covariant velocitycomponents
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Seismic wavefield modeling in media with fluid-filled fractures and surface topography 被引量:2
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作者 兰海强 张中杰 《Applied Geophysics》 SCIE CSCD 2012年第3期301-312,361,共13页
We present a finite difference (FD) method for the simulation of seismic wave fields in fractured medium with an irregular (non-fiat) free surface which is beneficial for interpreting exploration data acquired in ... We present a finite difference (FD) method for the simulation of seismic wave fields in fractured medium with an irregular (non-fiat) free surface which is beneficial for interpreting exploration data acquired in mountainous regions. Fractures are introduced through the Coates-Schoenberg approach into the FD scheme which leads to local anisotropic properties of the media where fractures are embedded. To implement surface topography, we take advantage of the boundary-conforming grid and map a rectangular grid onto a curved one. We use a stable and explicit second-order accurate finite difference scheme to discretize the elastic wave equations (in a curvilinear coordinate system) in a 2D heterogeneous transversely isotropic medium with a horizontal axis of symmetry (HTI). Efficiency tests performed by different numerical experiments clearly illustrate the influence of an irregular free surface on seismic wave propagation in fractured media which may be significant to mountain seismic exploration. The tests also illustrate that the scattered waves induced by the tips of the fracture are re-scattered by the features of the free surface topography. The scattered waves provoked by the topography are re-scattered by the fractures, especially Rayleigh wave scattering whose amplitudes are much larger than others and making it very difficult to identify effective information from the fractures. 展开更多
关键词 finite difference MODELING FRACTURE irregular free surface curvilinear coordinate
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Mathematical Models for Combined Refraction-Diffraction of Waves on Non-Uniform Current and Depth 被引量:35
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作者 Hong Guangwen Professor, Research Institute of Coastal and Ocean Engineering, Hohai University, 1 Xikang Road, Nanjing 210024 《China Ocean Engineering》 SCIE EI 1996年第4期433-454,共22页
Two mathematical models for combined refraction-diffraction of regular and irregular waves on non-uniform current in water of slowly varying topography are presented in this paper. Model I is derived by wave theory an... Two mathematical models for combined refraction-diffraction of regular and irregular waves on non-uniform current in water of slowly varying topography are presented in this paper. Model I is derived by wave theory and variational principle separately. It has two kinds of expressions including the dissipation term. Model n is based on the energy conservation equation with energy flux through the wave crest lines in orthogonal curvilinear coordinates and the wave kinematic conservation equation. The analysis and comparison and special cases of these two models are also given. 展开更多
关键词 refraction-diffraction DISSIPATION wave action conservation eikonal equation time-dependent ild slope equation orthogonal curvilinear coordinates
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New Eulerian-Lagrangian Method for Salinity Calculation 被引量:4
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作者 朱首贤 丁平兴 +2 位作者 沙文钰 冯芒 张文静 《China Ocean Engineering》 SCIE EI 2001年第4期553-564,共12页
A difference scheme in curvilinear coordinates is put forward for calculation of salinity in estuaries and coastal waters, which is based on Eulerian-Lagrangian method. It combines first-order and second-order Lagrang... A difference scheme in curvilinear coordinates is put forward for calculation of salinity in estuaries and coastal waters, which is based on Eulerian-Lagrangian method. It combines first-order and second-order Lagrangian interpolation to reduce numerical dispersion and oscillation. And the length of the curvilinear grid is also considered in the interpolation. Then the scheme is used in estuary, coast and ocean model, and several numerical experiments for the Yangtze Estuary and the Hangzhou Bay are conducted to test it. These experiments show that it is suitable for simulations of salinity in estuaries and coastal waters with the models using curvilinear coordinates. 展开更多
关键词 convection-dispersion Eulerian-Lagrangian method Lagrangian interpolation curvilinear coordinates
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