A high order finite difference numerical scheme is developed for the shallow water equations on curvilinear meshes based on an alternative flux formulation of the weighted essentially non-oscillatory(WENO)scheme.The e...A high order finite difference numerical scheme is developed for the shallow water equations on curvilinear meshes based on an alternative flux formulation of the weighted essentially non-oscillatory(WENO)scheme.The exact C-property is investigated,and comparison with the standard finite difference WENO scheme is made.Theoretical derivation and numerical results show that the proposed finite difference WENO scheme can maintain the exact C-property on both stationarily and dynamically generalized coordinate systems.The Harten-Lax-van Leer type flux is developed on general curvilinear meshes in two dimensions and verified on a number of benchmark problems,indicating smaller errors compared with the Lax-Friedrichs solver.In addition,we propose a positivity-preserving limiter on stationary meshes such that the scheme can preserve the non-negativity of the water height without loss of mass conservation.展开更多
Complex variables method has been used to solve the first and second fundamental problems for an infinite plate weakened by a generalized curvilinear hole C. The curvilinear hole is conformally mapped on the domain ou...Complex variables method has been used to solve the first and second fundamental problems for an infinite plate weakened by a generalized curvilinear hole C. The curvilinear hole is conformally mapped on the domain outside or inside a unit circle γ using a general rational mapping function with complex constants. Many special and new cases are derived from this work. Some of the work of the previous authors in this domain will be considered as special cases of this paper. Also the interesting cases when the shape of the hole takes different famous shapes are included. The components of stresses for some examples are obtained.展开更多
The method of automatically generating generalized curvilinear meshes has many advantages and is beginning to be used in ocean simulations. This three dimensional (3 D) coastal barotropic model in generalized curvilin...The method of automatically generating generalized curvilinear meshes has many advantages and is beginning to be used in ocean simulations. This three dimensional (3 D) coastal barotropic model in generalized curvilinear grids was developed to simulate the M 2, S 2, K 1 and O 1 tidal waves in the Bohai Sea, China. The numerical results agreeing with observations showed that the method is an effective tool for improving accuracy of simulations in shallow shelf seas, especially in the near coast region, if the pseudo effect there usually caused by rectangular grids can be removed.展开更多
It is explored that the line integral is a path independent in two or three arbitrary dimensional orthogonal curvilinear coordinate systems, which is based on the integral condition with the path independent in two or...It is explored that the line integral is a path independent in two or three arbitrary dimensional orthogonal curvilinear coordinate systems, which is based on the integral condition with the path independent in two or three dimensional rectangular coordinate systems. Firstly, according to the coordinate transformation, the condition that the line integral is the path independent in the polar coordinate system is obtained easily from the Green's theorem in two-dimensional rectangular coordinate system and the condition is extended to arbitrary two-dimension orthogonal curvilinear coordinates. Secondly, through the coordinate transformation relationship and the area projection method, the Stokes formula in three-dimensional rectangular coordinate system is promoted to the spherical coordinate system and cylindrical coordinate system, and the condition that the line integral is a path independent is obtained. Furthermore, the condition is extended to arbitrary three-dimension orthogonal curvilinear coordinates. Lastly, the conclusions are made.展开更多
AIM: To compare the corneal endothelial cell counts pre-and post-operation, ultrastructure of anterior lens capsule and surgical completion after diathermic highfrequency capsulorhexis(DHC) and continuous curvilinear ...AIM: To compare the corneal endothelial cell counts pre-and post-operation, ultrastructure of anterior lens capsule and surgical completion after diathermic highfrequency capsulorhexis(DHC) and continuous curvilinear capsulorrhexis(CCC) applied in phacoemulsification(PHACO) of white cataract surgery.METHODS: Sixty-six eyes of 66 patients(33 males and 33 females) with cataract aged between 60 and 80 y(mean 72.5±5.5) were recruited and undergone the surgery from June 2014 to November 2016. Anterior lens capsule, derived from two kinds of capsulorhexis, were randomly divided into two groups according to random number table. The ultrastructure of the capsule edge and its closer tissue were observed by transmission electron microscopy(TEM) and optical microscopy respectively. The surgical completion conditions and corneal endothelial cell counts were analyzed pre-and post-operation after two capsulorhexis.RESULTS: The capsule derived from CCC had smooth edge, well-organized cellular structure and the cells filling into the cutting edge under TEM and optical microscopy. The capsule derived from DHC had an approximate 60 banded area of cell degeneration and necrosis, with dentiform prominences at the edge of the capsule, and no cell structure was observed at this area. The corneal endothelial cell counts of both groups were slightly declined 1 wk post-operation compared with that of preoperation. There was no statistical difference between the two groups(t=1.63, P>0.05).CONCLUSION: DHC shows good clinical value in white mature and hypermature cataract surgery.展开更多
Explicit structure-preserving geometric particle-in-cell(PIC)algorithm in curvilinear orthogonal coordinate systems is developed.The work reported represents a further development of the structure-preserving geometric...Explicit structure-preserving geometric particle-in-cell(PIC)algorithm in curvilinear orthogonal coordinate systems is developed.The work reported represents a further development of the structure-preserving geometric PIC algorithm achieving the goal of practical applications in magnetic fusion research.The algorithm is constructed by discretizing the field theory for the system of charged particles and electromagnetic field using Whitney forms,discrete exterior calculus,and explicit non-canonical symplectic integration.In addition to the truncated infinitely dimensional symplectic structure,the algorithm preserves exactly many important physical symmetries and conservation laws,such as local energy conservation,gauge symmetry and the corresponding local charge conservation.As a result,the algorithm possesses the long-term accuracy and fidelity required for first-principles-based simulations of the multiscale tokamak physics.The algorithm has been implemented in the Sym PIC code,which is designed for highefficiency massively-parallel PIC simulations in modern clusters.The code has been applied to carry out whole-device 6 D kinetic simulation studies of tokamak physics.A self-consistent kinetic steady state for fusion plasma in the tokamak geometry is numerically found with a predominately diagonal and anisotropic pressure tensor.The state also admits a steady-state subsonic ion flow in the range of 10 km s-1,agreeing with experimental observations and analytical calculations Kinetic ballooning instability in the self-consistent kinetic steady state is simulated.It is shown that high-n ballooning modes have larger growth rates than low-n global modes,and in the nonlinear phase the modes saturate approximately in 5 ion transit times at the 2%level by the E×B flow generated by the instability.These results are consistent with early and recent electromagnetic gyrokinetic simulations.展开更多
In this work, we used the complex variable methods to derive the Goursat functions for the first and second fundamental problem of an infinite plate with a curvilinear hole C. The hole is mapped in the domain inside a...In this work, we used the complex variable methods to derive the Goursat functions for the first and second fundamental problem of an infinite plate with a curvilinear hole C. The hole is mapped in the domain inside a unit circle by means of the rational mapping function. Many special cases are discussed and established of these functions. Also, many applications and examples are considered. The results indicate that the infinite plate with a curvilinear hole inside the unit circle is very pronounced.展开更多
This paper seeks to develop an efficient multigrid algorithm for solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in L-shaped geometry.For this,the differential equations were di...This paper seeks to develop an efficient multigrid algorithm for solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in L-shaped geometry.For this,the differential equations were discretized by Finite Volume Method(FVM)with second-order approximation scheme and deferred correction.Moreover,the algebraic method and the differential method were used to generate the non-orthogonal structured curvilinear grids.Furthermore,the influence of some parameters of geometric multigrid method,as well as lexicographical Gauss–Seidel(Lex-GS),η-line Gauss–Seidel(η-line-GS),Modified Strongly Implicit(MSI)and modified incomplete LU decomposition(MILU)solvers on the Central Processing Unit(CPU)time was investigated.Therefore,several parameters of multigrid method and solvers were tested for the problem,with the use of nonorthogonal structured curvilinear grids and multigrid method,resulting in an algorithm with the combination that achieved the best results and CPU time.The geometric multigrid method with Full Approximation Scheme(FAS),V-cycle and standard coarsening ratio for this problem were utilized.This article shows how to calculate the coordinates transformation metrics in the coarser grids.Results show that the MSI and MILU solvers are the most efficient.Moreover,theMSI solver is faster thanMILU for both grids generators;and the solutions are more accurate for the Burgers problem with grids generated using elliptic equations.展开更多
A great number of semi-analytical models, notably the representation of electromagnetic fields by integral equations are based on the second order vector potential (SOVP) formalism which introduces two scalar potentia...A great number of semi-analytical models, notably the representation of electromagnetic fields by integral equations are based on the second order vector potential (SOVP) formalism which introduces two scalar potentials in order to obtain analytical expressions of the electromagnetic fields from the two potentials. However, the scalar decomposition is often known for canonical coordinate systems. This paper aims in introducing a specific SOVP formulation dedicated to arbitrary non-orthogonal curvilinear coordinates systems. The electromagnetic field representation which is derived in this paper constitutes the key stone for the development of semi-analytical models for solving some eddy currents moelling problems and electromagnetic radiation problems considering at least two homogeneous media separated by a rough interface. This SOVP formulation is derived from the tensor formalism and Maxwell’s equations written in a non-orthogonal coordinates system adapted to a surface characterized by a 2D arbitrary aperiodic profile.展开更多
In the present paper Cauchy integral methods have been applied to derive exact and expressions for Goursat’s function for the first and second fundamental problems of isotropic homogeneous perforated infinite elastic...In the present paper Cauchy integral methods have been applied to derive exact and expressions for Goursat’s function for the first and second fundamental problems of isotropic homogeneous perforated infinite elastic media in the presence of uniform flow of heat. For this, we considered the problem of a thin infinite plate of specific thickness with a curvilinear hole where the origins lie in the hole is conformally mapped outside a unit circle by means of a specific rational mapping. Moreover, the three stress components σxx, σyy and σxy of the boundary value problem in the thermoelasticity plane are obtained. Many special cases of the conformal mapping and four applications for different cases are discussed and many main results are derived from the work.展开更多
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
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 inaccura...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 coordinates show good agreement with the data obtained in three typical physical experiments,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
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
The velocity field in meandering compound channels with overbank 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 overbank 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-ε turbulence hydrodynamic model in curvilinear coordinates is established to simulate the overbank flow. The body-fitted 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 overbank flow.展开更多
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 dissipa...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 employed 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 matrix can make the transformed equations relatively concise,the treatment of lateral boundary conditions easier and the development 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
The original nonlinear chirp scaling(NCS) algorithm was extended for high precision processing of the highly squinted curvilinear trajectory synthetic aperture radar(CTSAR).Based on the analysis of slant range model a...The original nonlinear chirp scaling(NCS) algorithm was extended for high precision processing of the highly squinted curvilinear trajectory synthetic aperture radar(CTSAR).Based on the analysis of slant range model and the frequency spectrum characteristics of the echo signal,a novel nonlinear chirp scaling function and more complex phase compensation factors with both velocity and acceleration parameters were proposed in the new algorithm for accommodation to curvilinear trajectory.The processing flow and computational complexity of modified NCS algorithm were fundamentally the same as the original NCS algorithm.However,the higher order phase compensation,range cell migration correction(RCMC) and range-variant secondary range compression(SRC) caused by the non-linear aperture and the severe range-azimuth coupling were accomplished accurately and efficiently without interpolation.Simulation results show that data acquired with a curvilinear aperture and a squint angle up to about 50° for X-band can be processed with no evident degradation of impulse response function.展开更多
基金the National Natural Science Foundation of China(11901555,11871448,12001009).
文摘A high order finite difference numerical scheme is developed for the shallow water equations on curvilinear meshes based on an alternative flux formulation of the weighted essentially non-oscillatory(WENO)scheme.The exact C-property is investigated,and comparison with the standard finite difference WENO scheme is made.Theoretical derivation and numerical results show that the proposed finite difference WENO scheme can maintain the exact C-property on both stationarily and dynamically generalized coordinate systems.The Harten-Lax-van Leer type flux is developed on general curvilinear meshes in two dimensions and verified on a number of benchmark problems,indicating smaller errors compared with the Lax-Friedrichs solver.In addition,we propose a positivity-preserving limiter on stationary meshes such that the scheme can preserve the non-negativity of the water height without loss of mass conservation.
文摘Complex variables method has been used to solve the first and second fundamental problems for an infinite plate weakened by a generalized curvilinear hole C. The curvilinear hole is conformally mapped on the domain outside or inside a unit circle γ using a general rational mapping function with complex constants. Many special and new cases are derived from this work. Some of the work of the previous authors in this domain will be considered as special cases of this paper. Also the interesting cases when the shape of the hole takes different famous shapes are included. The components of stresses for some examples are obtained.
文摘The method of automatically generating generalized curvilinear meshes has many advantages and is beginning to be used in ocean simulations. This three dimensional (3 D) coastal barotropic model in generalized curvilinear grids was developed to simulate the M 2, S 2, K 1 and O 1 tidal waves in the Bohai Sea, China. The numerical results agreeing with observations showed that the method is an effective tool for improving accuracy of simulations in shallow shelf seas, especially in the near coast region, if the pseudo effect there usually caused by rectangular grids can be removed.
基金Funded by the Natural Science Foundation Project of CQCSTC(No.cstc2012jj A50018)the Basic Research of Chongqing Municipal Education Commission(No.KJ120631)the Science Research Foundation Project of CQNU(No.16XYY31)
文摘It is explored that the line integral is a path independent in two or three arbitrary dimensional orthogonal curvilinear coordinate systems, which is based on the integral condition with the path independent in two or three dimensional rectangular coordinate systems. Firstly, according to the coordinate transformation, the condition that the line integral is the path independent in the polar coordinate system is obtained easily from the Green's theorem in two-dimensional rectangular coordinate system and the condition is extended to arbitrary two-dimension orthogonal curvilinear coordinates. Secondly, through the coordinate transformation relationship and the area projection method, the Stokes formula in three-dimensional rectangular coordinate system is promoted to the spherical coordinate system and cylindrical coordinate system, and the condition that the line integral is a path independent is obtained. Furthermore, the condition is extended to arbitrary three-dimension orthogonal curvilinear coordinates. Lastly, the conclusions are made.
基金Supported by the Shaanxi Provincial Department of Science and Technology Agency Project (No.2017SF-288)
文摘AIM: To compare the corneal endothelial cell counts pre-and post-operation, ultrastructure of anterior lens capsule and surgical completion after diathermic highfrequency capsulorhexis(DHC) and continuous curvilinear capsulorrhexis(CCC) applied in phacoemulsification(PHACO) of white cataract surgery.METHODS: Sixty-six eyes of 66 patients(33 males and 33 females) with cataract aged between 60 and 80 y(mean 72.5±5.5) were recruited and undergone the surgery from June 2014 to November 2016. Anterior lens capsule, derived from two kinds of capsulorhexis, were randomly divided into two groups according to random number table. The ultrastructure of the capsule edge and its closer tissue were observed by transmission electron microscopy(TEM) and optical microscopy respectively. The surgical completion conditions and corneal endothelial cell counts were analyzed pre-and post-operation after two capsulorhexis.RESULTS: The capsule derived from CCC had smooth edge, well-organized cellular structure and the cells filling into the cutting edge under TEM and optical microscopy. The capsule derived from DHC had an approximate 60 banded area of cell degeneration and necrosis, with dentiform prominences at the edge of the capsule, and no cell structure was observed at this area. The corneal endothelial cell counts of both groups were slightly declined 1 wk post-operation compared with that of preoperation. There was no statistical difference between the two groups(t=1.63, P>0.05).CONCLUSION: DHC shows good clinical value in white mature and hypermature cataract surgery.
基金supported by the the National MCF Energy R&D Program(No.2018YFE0304100)National Key Research and Development Program(Nos.2016YFA0400600,2016YFA0400601 and 2016YFA0400602)+1 种基金National Natural Science Foundation of China(Nos.11905220 and 11805273)supported by the U.S.Department of Energy(DE-AC02-09CH11466)。
文摘Explicit structure-preserving geometric particle-in-cell(PIC)algorithm in curvilinear orthogonal coordinate systems is developed.The work reported represents a further development of the structure-preserving geometric PIC algorithm achieving the goal of practical applications in magnetic fusion research.The algorithm is constructed by discretizing the field theory for the system of charged particles and electromagnetic field using Whitney forms,discrete exterior calculus,and explicit non-canonical symplectic integration.In addition to the truncated infinitely dimensional symplectic structure,the algorithm preserves exactly many important physical symmetries and conservation laws,such as local energy conservation,gauge symmetry and the corresponding local charge conservation.As a result,the algorithm possesses the long-term accuracy and fidelity required for first-principles-based simulations of the multiscale tokamak physics.The algorithm has been implemented in the Sym PIC code,which is designed for highefficiency massively-parallel PIC simulations in modern clusters.The code has been applied to carry out whole-device 6 D kinetic simulation studies of tokamak physics.A self-consistent kinetic steady state for fusion plasma in the tokamak geometry is numerically found with a predominately diagonal and anisotropic pressure tensor.The state also admits a steady-state subsonic ion flow in the range of 10 km s-1,agreeing with experimental observations and analytical calculations Kinetic ballooning instability in the self-consistent kinetic steady state is simulated.It is shown that high-n ballooning modes have larger growth rates than low-n global modes,and in the nonlinear phase the modes saturate approximately in 5 ion transit times at the 2%level by the E×B flow generated by the instability.These results are consistent with early and recent electromagnetic gyrokinetic simulations.
文摘In this work, we used the complex variable methods to derive the Goursat functions for the first and second fundamental problem of an infinite plate with a curvilinear hole C. The hole is mapped in the domain inside a unit circle by means of the rational mapping function. Many special cases are discussed and established of these functions. Also, many applications and examples are considered. The results indicate that the infinite plate with a curvilinear hole inside the unit circle is very pronounced.
文摘This paper seeks to develop an efficient multigrid algorithm for solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in L-shaped geometry.For this,the differential equations were discretized by Finite Volume Method(FVM)with second-order approximation scheme and deferred correction.Moreover,the algebraic method and the differential method were used to generate the non-orthogonal structured curvilinear grids.Furthermore,the influence of some parameters of geometric multigrid method,as well as lexicographical Gauss–Seidel(Lex-GS),η-line Gauss–Seidel(η-line-GS),Modified Strongly Implicit(MSI)and modified incomplete LU decomposition(MILU)solvers on the Central Processing Unit(CPU)time was investigated.Therefore,several parameters of multigrid method and solvers were tested for the problem,with the use of nonorthogonal structured curvilinear grids and multigrid method,resulting in an algorithm with the combination that achieved the best results and CPU time.The geometric multigrid method with Full Approximation Scheme(FAS),V-cycle and standard coarsening ratio for this problem were utilized.This article shows how to calculate the coordinates transformation metrics in the coarser grids.Results show that the MSI and MILU solvers are the most efficient.Moreover,theMSI solver is faster thanMILU for both grids generators;and the solutions are more accurate for the Burgers problem with grids generated using elliptic equations.
文摘A great number of semi-analytical models, notably the representation of electromagnetic fields by integral equations are based on the second order vector potential (SOVP) formalism which introduces two scalar potentials in order to obtain analytical expressions of the electromagnetic fields from the two potentials. However, the scalar decomposition is often known for canonical coordinate systems. This paper aims in introducing a specific SOVP formulation dedicated to arbitrary non-orthogonal curvilinear coordinates systems. The electromagnetic field representation which is derived in this paper constitutes the key stone for the development of semi-analytical models for solving some eddy currents moelling problems and electromagnetic radiation problems considering at least two homogeneous media separated by a rough interface. This SOVP formulation is derived from the tensor formalism and Maxwell’s equations written in a non-orthogonal coordinates system adapted to a surface characterized by a 2D arbitrary aperiodic profile.
文摘In the present paper Cauchy integral methods have been applied to derive exact and expressions for Goursat’s function for the first and second fundamental problems of isotropic homogeneous perforated infinite elastic media in the presence of uniform flow of heat. For this, we considered the problem of a thin infinite plate of specific thickness with a curvilinear hole where the origins lie in the hole is conformally mapped outside a unit circle by means of a specific rational mapping. Moreover, the three stress components σxx, σyy and σxy of the boundary value problem in the thermoelasticity plane are obtained. Many special cases of the conformal mapping and four applications for different cases are discussed and many main results are derived from the work.
文摘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.
基金supported by the National Basic Research Program of China ( Grant No.2006CB403302)the National Natural Science Foundation of China (Grant Nos .50839001 and 50709004)the Scientific Research Foundation of the Higher Education Institutions of Liaoning Province (Grant No.2006T018)
文摘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 coordinates show good agreement with the data obtained in three typical physical experiments,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.
基金supported by the National Natural Science Foundation of China (Grant Nos. 50839001 and 50979036)
文摘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.
文摘The velocity field in meandering compound channels with overbank 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-ε turbulence hydrodynamic model in curvilinear coordinates is established to simulate the overbank flow. The body-fitted 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 overbank flow.
基金supported by the National Natural Science Foundation of China (Grant Nos .51079082 and 40676053)State Key Laboratory of Ocean Engineering ( Grant Nos . GKZD010012, GP010818 and GKZD010024)
文摘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 employed 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 matrix can make the transformed equations relatively concise,the treatment of lateral boundary conditions easier and the development 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.
基金Project(61171133) supported by the National Natural Science Foundation of ChinaProject(61101182) supported by the National Natural Science Foundation for Young Scientists of ChinaProject(11JJ1010) supported by the Natural Science Foundation for Distinguished Young Scholars of Hunan Province,China
文摘The original nonlinear chirp scaling(NCS) algorithm was extended for high precision processing of the highly squinted curvilinear trajectory synthetic aperture radar(CTSAR).Based on the analysis of slant range model and the frequency spectrum characteristics of the echo signal,a novel nonlinear chirp scaling function and more complex phase compensation factors with both velocity and acceleration parameters were proposed in the new algorithm for accommodation to curvilinear trajectory.The processing flow and computational complexity of modified NCS algorithm were fundamentally the same as the original NCS algorithm.However,the higher order phase compensation,range cell migration correction(RCMC) and range-variant secondary range compression(SRC) caused by the non-linear aperture and the severe range-azimuth coupling were accomplished accurately and efficiently without interpolation.Simulation results show that data acquired with a curvilinear aperture and a squint angle up to about 50° for X-band can be processed with no evident degradation of impulse response function.
