The initial stresses widely exist in elastic materials.While achieving a continuum stress-free configuration through compatible unloading is desirable,mechanical unloading alone frequently proves insufficient,posing c...The initial stresses widely exist in elastic materials.While achieving a continuum stress-free configuration through compatible unloading is desirable,mechanical unloading alone frequently proves insufficient,posing challenges in avoiding virtual stress-free configurations.In this paper,we introduce a novel concept of equivalent temperature variation to counteract the incompatible initial strain.Our focus is on initially stressed cylindrical and spherical elastomers,where we first derive the Saint-Venant,Beltrami-Michell,and Volterra integral conditions in orthogonal curvilinear coordinates using the exterior differential form theory.It is shown that for any given axially or spherically distributed initial stress,an equivalent temperature variation always exists.Furthermore,we propose two innovative initial stress forms based on the steady-state heat conduction.By introducing an equivalent temperature variation,the initial stress can be released through a compatible thermo-mechanical unloading process,offering valuable insights into the constitutive theory of initially stressed elastic materials.展开更多
We give a proof of an explicit formula for affine coodinates of points in the Sato’s infinite Grassmannian corresponding to tau-functions for the KdV hierarchy.
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
This study was an effort to calculate geographic coordinates, solar horizontal and equatorial cooridnates, direction of Qibla, sizes of Earth and Sun through gnomon (a vertical stick casting shadow). Gnomon has been u...This study was an effort to calculate geographic coordinates, solar horizontal and equatorial cooridnates, direction of Qibla, sizes of Earth and Sun through gnomon (a vertical stick casting shadow). Gnomon has been used in history for remote navigations, astronomical and geodetic measurements. Geographic coordinates were found out with accuracy of less than 0.19 decimal degree from gnomon. Sun’s horizontal and equatorial coordinates were calculated and analyzed with US Navy Observatory and NOAA Earth System Research Laboratory. These coordinates were less than 0.01 decimal degree different from coordinates provided by US Navy and following same daily trend with time. Through spherical triangle, direction of Qibla was found out. And it came out less than 0.18 decimal degree different from its value, used in Lahore. Radius of the earth measured from gnomon using concepts of Al Buruni was 1.45 km different from its true value. Using geometrical technique of similar and concurrent triangles, size of the sun was calculated and it was 1,651,088.776 km. Investigation of systematic and random errors in each calculation was the part of this research.展开更多
This article shows that in spherical polar coordinates, some noncentral separable potentials have super-symmetry and shape invariance in the r and θ dimensions, we choose Hartmann potential and ring-shaped oscillator...This article shows that in spherical polar coordinates, some noncentral separable potentials have super-symmetry and shape invariance in the r and θ dimensions, we choose Hartmann potential and ring-shaped oscillator astwo important examples, thus in principle the energy eigenvalues and energy eigenfunctions of such the potentials in ther and θ dimensions can be obtained by the method of supersymmetric quantum mechanics. Here we use an alternativemethod to get the required results.展开更多
Based on FDTD difference expressions and eigenfunctions of Maxwell functions in cylindrical coordinates, mesh wave impedances (MWIs) in 2D and 3D cylindrical coordinates were introduced. Combined with the concept of p...Based on FDTD difference expressions and eigenfunctions of Maxwell functions in cylindrical coordinates, mesh wave impedances (MWIs) in 2D and 3D cylindrical coordinates were introduced. Combined with the concept of perfectly matched layer (PML), MWI PML absorbing boundary condition (ABC) algorithm was deduced in 2D cylindrical coordinates. Numerical experiments were done to investigate the validity of MWI and its application in cylindrical coordinates FDTD algorithm. The results showed that MWI in cylindrical coordinates can be used to accurately calculate the numerical reflection error caused by different mesh increments in non uniform FDTD. MWI can also provide theoretical criterion to define the permitted variable range of mesh dimension. MWI PML ABC is easy to be applied and reduces low numerical reflection, which only causes a little higher reflection error compared with Teixeira's PML.展开更多
The principle and accuracy of 3-D coordinates acquisition using one single camera and the Aided Measuring Probe(AMP) are discussed in this paper. Using one single camera and one AMP which has several embedded targets ...The principle and accuracy of 3-D coordinates acquisition using one single camera and the Aided Measuring Probe(AMP) are discussed in this paper. Using one single camera and one AMP which has several embedded targets and one tip with known coordinates, the single camera′s orientation and location can be calculated. After orientation, the global coordinate system is obtained. During measurement, the camera is fixed firstly, then the AMP is held and the feature point is touched.The camera is triggered lastly. The position and orientation of the AMP are therefore calculated from the size and position of its image on the sensor. Since the tip point of AMP has known relation with the embedded targets, the feature point can be measured. Tests show that the accuracy of length measurement is 0.2 mm and accuracy for flatness measurement in XSY-plane is 0.1 mm.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 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
The classical natural coordinate modeling method which removes the Euler angles and Euler parameters from the governing equations is particularly suitable for the sensitivity analysis and optimization of multibody sys...The classical natural coordinate modeling method which removes the Euler angles and Euler parameters from the governing equations is particularly suitable for the sensitivity analysis and optimization of multibody systems. However, the formulation has so many principles in choosing the generalized coordinates that it hinders the implementation of modeling automation, A first order direct sensitivity analysis approach to multibody systems formulated with novel natural coordinates is presented. Firstly, a new selection method for natural coordinate is developed. The method introduces 12 coordinates to describe the position and orientation of a spatial object. On the basis of the proposed natural coordinates, rigid constraint conditions, the basic constraint elements as well as the initial conditions for the governing equations are derived. Considering the characteristics of the governing equations, the newly proposed generalized-ct integration method is used and the corresponding algorithm flowchart is discussed. The objective function, the detailed analysis process of first order direct sensitivity analysis and related solving strategy are provided based on the previous modeling system Finally, in order to verify the validity and accuracy of the method presented, the sensitivity analysis of a planar spinner-slider mechanism and a spatial crank-slider mechanism are conducted. The test results agree well with that of the finite difference method, and the maximum absolute deviation of the results is less than 3%. The proposed approach is not only convenient for automatic modeling, but also helpful for the reduction of the complexity of sensitivity analysis, which provides a practical and effective way to obtain sensitivity for the optimization problems of multibody systems.展开更多
A new oceanic general circulation model in pressure coordinates is formulated. Since the bottom pressure changes with time, the vertical coordinate is actually a pressure-sigma coordinate. The numerical solution of th...A new oceanic general circulation model in pressure coordinates is formulated. Since the bottom pressure changes with time, the vertical coordinate is actually a pressure-sigma coordinate. The numerical solution of the model is based on an energy-conservation scheme of finite difference. The most important new feature of the model is that it is a truly compressible ocean model and it is free of the Boussinesq approximations. Thus, the new model is quite different from many existing models in the following ways: 1) the exact form of mass conservation, 2) the in-situ instantaneous pressure and the UNESCO equation of state to calculate density, 3) the in-situ density in the momentum. equations, 4) finite difference schemes that conserve the total energy. Initial tests showed that the model code runs smoothly, and it is quite stable. The quasi-steady circulation patterns generated by the new model compare well with existing models, but the time evolution of the new model seems different from some existing models. Thus, the non-Boussinesq models may provide more accurate information for climate study and satellite observations.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 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
An FDTD system associated with uniaxial perfectly matched layer（UPML） for an electromagnetic scattering problem in two-dimensional space in polar coordinates is considered.Particularly the FDTD system of an initial-...An FDTD system associated with uniaxial perfectly matched layer（UPML） for an electromagnetic scattering problem in two-dimensional space in polar coordinates is considered.Particularly the FDTD system of an initial-boundary value problems of the transverse magnetic（TM） mode to Maxwell＇s equations is obtained by Yee＇s algorithm,and the open domain of the scattering problem is truncated by a circle with a UPML.Besides,an artificial boundary condition is imposed on the outer boundary of the UPML.Afterwards,stability of the FDTD system on the truncated domain is established through energy estimates by the Gronwall inequality.Numerical experiments are designed to approve the theoretical analysis.展开更多
Aim To study the Lie symmetries and the consered quantities of the holonomic systems with remainder coordinates. Methods Using the invariance of the ordinary differential equations under the infinitesimal transformati...Aim To study the Lie symmetries and the consered quantities of the holonomic systems with remainder coordinates. Methods Using the invariance of the ordinary differential equations under the infinitesimal transformations to establish the determining equations and the restriction equations of the Lie symmetries of the systems. Results and Conclusion the structure equation and the form of conserved quantities were obtained. An example was given to illustrate the application of the result.展开更多
Traditional multiframe Track-Before-Detect(TBD)may incur adverse integration loss resulting from model mismatch in sensor coordinates.Its suboptimal integration strategy may cause target envelope degradation.To addres...Traditional multiframe Track-Before-Detect(TBD)may incur adverse integration loss resulting from model mismatch in sensor coordinates.Its suboptimal integration strategy may cause target envelope degradation.To address these issues,a pseudo-spectrum-based multiframe TBD in mixed coordinates is proposed firstly.The data search for energy integration is conducted based on an accurate model in the x-y plane while target energy is integrated based on pseudo-spectrum in sensor coordinates.The algorithm performance is improved since the model mismatch is eliminated,and the pseudo-spectrum based integration facilitates well maintained target envelope.The detailed multiframe integration procedure and theoretical target integrated envelope are derived.Secondly,to cope with the unknown target velocity,a velocity filter bank based on pseudo-spectrum in mixed coordinates is proposed.The effect of velocity mismatch on algorithm performance is analyzed and an efficient method for filter bank design is presented.Thirdly,a parameter estimation method using characteristics of integrated envelope is presented for improved target polar position and Cartesian velocity estimation.Finally,numerical results are provided to demonstrate the effectiveness of the proposed method.展开更多
A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous H...A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous Hamiltonian system is multiplied by a set of multiplicative functions, then the general expression of the first integral can be obtained, An example is given to illustrate the application of the results.展开更多
In shallow coastal regions where water surface fluctuations are non-negligible compared to the mean water depth,the use of sigma coordinates allows the calculation of residual velocity around the mean water surface le...In shallow coastal regions where water surface fluctuations are non-negligible compared to the mean water depth,the use of sigma coordinates allows the calculation of residual velocity around the mean water surface level.Theoretical analysis and generic numerical experiments were conducted to understand the physical meaning of the residual velocities at sigma layers in breadth-averaged tidal channels.For shallow water waves,the sigma layers coincide with the water wave surfaces within the water column such that the Stokes velocity and its vertical and horizontal components can be expressed in discrete forms using the sigma velocity.The residual velocity at a sigma layer is the sum of the Eulerian velocity and the vertical component of the Stokes velocity at the mean depth of the sigma layer and,therefore,can be referred to as a semi-Lagrangian residual velocity.Because the vertical component of the Stokes velocity is one order of magnitude smaller than the horizontal component,the sigma residual velocity approximates the Eulerian residual velocity.The residual transport velocity at a sigma layer is the sum of the sigma residual velocity and the horizontal component of the Stokes velocity and approximates the Lagrangian residual velocity in magnitude and direction,but the two residual velocities are not conceptually the same.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 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
Mesh deformation technique is widely used in many application fields, and has re- ceived a lot of attentions in recent years. This paper focuses on the methodology and algorithm of algebraic type mesh deformation for ...Mesh deformation technique is widely used in many application fields, and has re- ceived a lot of attentions in recent years. This paper focuses on the methodology and algorithm of algebraic type mesh deformation for unstructured mesh in numerical discretization. To preserve mesh quality effectively, an algebraic approach for two and three dimensional unstructured mesh is developed based on mean value coordinates interpolation combined with node visibility analysis. The proposed approach firstly performs node visibility analysis to find out the visible boundary for each grid point to be moved, then evaluates the mean value coordinates of each grid point with respect to all vertices on its visible boundary. Thus the displacements of grid points can be calculated by interpolating the boundary movement by the mean value coordinates. Compared with other methods, the proposed method has good deformation capability and predictable com- putational cost, with no need to select parameters or functions. Applications of mesh deformation in different fields are presented to demonstrate the effectiveness of the proposed approach. The results of numerical experiments exhibit not only superior deformation capability of the method in traditional applications of fluid dynamic grid, but also great potential in modeling for large deformation analysis and inverse design problems.展开更多
This paper introduces the canonical coordinates method to obtain the first integral of a single-degree freedom constraint mechanical system that contains conserva-tive and non-conservative constraint homonomic systems...This paper introduces the canonical coordinates method to obtain the first integral of a single-degree freedom constraint mechanical system that contains conserva-tive and non-conservative constraint homonomic systems. The definition and properties of canonical coordinates are introduced. The relation between Lie point symmetries and the canonical coordinates of the constraint mechanical system are expressed. By this re-lation, the canonical coordinates can be obtained. Properties of the canonical coordinates and the Lie symmetry theory are used to seek the first integrals of constraint mechanical system. Three examples are used to show applications of the results.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.12241205 and 12032019)the National Key Research and Development Program of China(No.2022YFA1203200)the Strategic Priority Research Program of Chinese Academy of Sciences(Nos.XDB0620101 and XDB0620103)。
文摘The initial stresses widely exist in elastic materials.While achieving a continuum stress-free configuration through compatible unloading is desirable,mechanical unloading alone frequently proves insufficient,posing challenges in avoiding virtual stress-free configurations.In this paper,we introduce a novel concept of equivalent temperature variation to counteract the incompatible initial strain.Our focus is on initially stressed cylindrical and spherical elastomers,where we first derive the Saint-Venant,Beltrami-Michell,and Volterra integral conditions in orthogonal curvilinear coordinates using the exterior differential form theory.It is shown that for any given axially or spherically distributed initial stress,an equivalent temperature variation always exists.Furthermore,we propose two innovative initial stress forms based on the steady-state heat conduction.By introducing an equivalent temperature variation,the initial stress can be released through a compatible thermo-mechanical unloading process,offering valuable insights into the constitutive theory of initially stressed elastic materials.
文摘We give a proof of an explicit formula for affine coodinates of points in the Sato’s infinite Grassmannian corresponding to tau-functions for the KdV hierarchy.
文摘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.
文摘This study was an effort to calculate geographic coordinates, solar horizontal and equatorial cooridnates, direction of Qibla, sizes of Earth and Sun through gnomon (a vertical stick casting shadow). Gnomon has been used in history for remote navigations, astronomical and geodetic measurements. Geographic coordinates were found out with accuracy of less than 0.19 decimal degree from gnomon. Sun’s horizontal and equatorial coordinates were calculated and analyzed with US Navy Observatory and NOAA Earth System Research Laboratory. These coordinates were less than 0.01 decimal degree different from coordinates provided by US Navy and following same daily trend with time. Through spherical triangle, direction of Qibla was found out. And it came out less than 0.18 decimal degree different from its value, used in Lahore. Radius of the earth measured from gnomon using concepts of Al Buruni was 1.45 km different from its true value. Using geometrical technique of similar and concurrent triangles, size of the sun was calculated and it was 1,651,088.776 km. Investigation of systematic and random errors in each calculation was the part of this research.
文摘This article shows that in spherical polar coordinates, some noncentral separable potentials have super-symmetry and shape invariance in the r and θ dimensions, we choose Hartmann potential and ring-shaped oscillator astwo important examples, thus in principle the energy eigenvalues and energy eigenfunctions of such the potentials in ther and θ dimensions can be obtained by the method of supersymmetric quantum mechanics. Here we use an alternativemethod to get the required results.
文摘Based on FDTD difference expressions and eigenfunctions of Maxwell functions in cylindrical coordinates, mesh wave impedances (MWIs) in 2D and 3D cylindrical coordinates were introduced. Combined with the concept of perfectly matched layer (PML), MWI PML absorbing boundary condition (ABC) algorithm was deduced in 2D cylindrical coordinates. Numerical experiments were done to investigate the validity of MWI and its application in cylindrical coordinates FDTD algorithm. The results showed that MWI in cylindrical coordinates can be used to accurately calculate the numerical reflection error caused by different mesh increments in non uniform FDTD. MWI can also provide theoretical criterion to define the permitted variable range of mesh dimension. MWI PML ABC is easy to be applied and reduces low numerical reflection, which only causes a little higher reflection error compared with Teixeira's PML.
文摘The principle and accuracy of 3-D coordinates acquisition using one single camera and the Aided Measuring Probe(AMP) are discussed in this paper. Using one single camera and one AMP which has several embedded targets and one tip with known coordinates, the single camera′s orientation and location can be calculated. After orientation, the global coordinate system is obtained. During measurement, the camera is fixed firstly, then the AMP is held and the feature point is touched.The camera is triggered lastly. The position and orientation of the AMP are therefore calculated from the size and position of its image on the sensor. Since the tip point of AMP has known relation with the embedded targets, the feature point can be measured. Tests show that the accuracy of length measurement is 0.2 mm and accuracy for flatness measurement in XSY-plane is 0.1 mm.
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 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.
基金supported by National Defense Pre-research Foundation of China during the 12th Five-Year Plan Period(Grant No.51036050107)
文摘The classical natural coordinate modeling method which removes the Euler angles and Euler parameters from the governing equations is particularly suitable for the sensitivity analysis and optimization of multibody systems. However, the formulation has so many principles in choosing the generalized coordinates that it hinders the implementation of modeling automation, A first order direct sensitivity analysis approach to multibody systems formulated with novel natural coordinates is presented. Firstly, a new selection method for natural coordinate is developed. The method introduces 12 coordinates to describe the position and orientation of a spatial object. On the basis of the proposed natural coordinates, rigid constraint conditions, the basic constraint elements as well as the initial conditions for the governing equations are derived. Considering the characteristics of the governing equations, the newly proposed generalized-ct integration method is used and the corresponding algorithm flowchart is discussed. The objective function, the detailed analysis process of first order direct sensitivity analysis and related solving strategy are provided based on the previous modeling system Finally, in order to verify the validity and accuracy of the method presented, the sensitivity analysis of a planar spinner-slider mechanism and a spatial crank-slider mechanism are conducted. The test results agree well with that of the finite difference method, and the maximum absolute deviation of the results is less than 3%. The proposed approach is not only convenient for automatic modeling, but also helpful for the reduction of the complexity of sensitivity analysis, which provides a practical and effective way to obtain sensitivity for the optimization problems of multibody systems.
文摘A new oceanic general circulation model in pressure coordinates is formulated. Since the bottom pressure changes with time, the vertical coordinate is actually a pressure-sigma coordinate. The numerical solution of the model is based on an energy-conservation scheme of finite difference. The most important new feature of the model is that it is a truly compressible ocean model and it is free of the Boussinesq approximations. Thus, the new model is quite different from many existing models in the following ways: 1) the exact form of mass conservation, 2) the in-situ instantaneous pressure and the UNESCO equation of state to calculate density, 3) the in-situ density in the momentum. equations, 4) finite difference schemes that conserve the total energy. Initial tests showed that the model code runs smoothly, and it is quite stable. The quasi-steady circulation patterns generated by the new model compare well with existing models, but the time evolution of the new model seems different from some existing models. Thus, the non-Boussinesq models may provide more accurate information for climate study and satellite observations.
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 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.
文摘An FDTD system associated with uniaxial perfectly matched layer（UPML） for an electromagnetic scattering problem in two-dimensional space in polar coordinates is considered.Particularly the FDTD system of an initial-boundary value problems of the transverse magnetic（TM） mode to Maxwell＇s equations is obtained by Yee＇s algorithm,and the open domain of the scattering problem is truncated by a circle with a UPML.Besides,an artificial boundary condition is imposed on the outer boundary of the UPML.Afterwards,stability of the FDTD system on the truncated domain is established through energy estimates by the Gronwall inequality.Numerical experiments are designed to approve the theoretical analysis.
文摘Aim To study the Lie symmetries and the consered quantities of the holonomic systems with remainder coordinates. Methods Using the invariance of the ordinary differential equations under the infinitesimal transformations to establish the determining equations and the restriction equations of the Lie symmetries of the systems. Results and Conclusion the structure equation and the form of conserved quantities were obtained. An example was given to illustrate the application of the result.
基金supported by the National Natural Science Foundation of China(No.61671181)。
文摘Traditional multiframe Track-Before-Detect(TBD)may incur adverse integration loss resulting from model mismatch in sensor coordinates.Its suboptimal integration strategy may cause target envelope degradation.To address these issues,a pseudo-spectrum-based multiframe TBD in mixed coordinates is proposed firstly.The data search for energy integration is conducted based on an accurate model in the x-y plane while target energy is integrated based on pseudo-spectrum in sensor coordinates.The algorithm performance is improved since the model mismatch is eliminated,and the pseudo-spectrum based integration facilitates well maintained target envelope.The detailed multiframe integration procedure and theoretical target integrated envelope are derived.Secondly,to cope with the unknown target velocity,a velocity filter bank based on pseudo-spectrum in mixed coordinates is proposed.The effect of velocity mismatch on algorithm performance is analyzed and an efficient method for filter bank design is presented.Thirdly,a parameter estimation method using characteristics of integrated envelope is presented for improved target polar position and Cartesian velocity estimation.Finally,numerical results are provided to demonstrate the effectiveness of the proposed method.
文摘A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous Hamiltonian system is multiplied by a set of multiplicative functions, then the general expression of the first integral can be obtained, An example is given to illustrate the application of the results.
基金The National Basic Research Program of China under contract No.2015CB954000the National Natural Science Foundation of China under contract No.41476004。
文摘In shallow coastal regions where water surface fluctuations are non-negligible compared to the mean water depth,the use of sigma coordinates allows the calculation of residual velocity around the mean water surface level.Theoretical analysis and generic numerical experiments were conducted to understand the physical meaning of the residual velocities at sigma layers in breadth-averaged tidal channels.For shallow water waves,the sigma layers coincide with the water wave surfaces within the water column such that the Stokes velocity and its vertical and horizontal components can be expressed in discrete forms using the sigma velocity.The residual velocity at a sigma layer is the sum of the Eulerian velocity and the vertical component of the Stokes velocity at the mean depth of the sigma layer and,therefore,can be referred to as a semi-Lagrangian residual velocity.Because the vertical component of the Stokes velocity is one order of magnitude smaller than the horizontal component,the sigma residual velocity approximates the Eulerian residual velocity.The residual transport velocity at a sigma layer is the sum of the sigma residual velocity and the horizontal component of the Stokes velocity and approximates the Lagrangian residual velocity in magnitude and direction,but the two residual velocities are not conceptually the same.
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 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.
基金Project supported by the National Basic Research Program of China(No.2010CB731503)the National Natural Science Foundation of China(Nos.11172004 and 10772004)the Beijing Municipal Natural Science Foundation(No.1102020)
文摘Mesh deformation technique is widely used in many application fields, and has re- ceived a lot of attentions in recent years. This paper focuses on the methodology and algorithm of algebraic type mesh deformation for unstructured mesh in numerical discretization. To preserve mesh quality effectively, an algebraic approach for two and three dimensional unstructured mesh is developed based on mean value coordinates interpolation combined with node visibility analysis. The proposed approach firstly performs node visibility analysis to find out the visible boundary for each grid point to be moved, then evaluates the mean value coordinates of each grid point with respect to all vertices on its visible boundary. Thus the displacements of grid points can be calculated by interpolating the boundary movement by the mean value coordinates. Compared with other methods, the proposed method has good deformation capability and predictable com- putational cost, with no need to select parameters or functions. Applications of mesh deformation in different fields are presented to demonstrate the effectiveness of the proposed approach. The results of numerical experiments exhibit not only superior deformation capability of the method in traditional applications of fluid dynamic grid, but also great potential in modeling for large deformation analysis and inverse design problems.
基金Project supported by the National Natural Science Foundation of China(Nos.11072218 and 11272287)the Program for Changjiang Scholars and Innovative Research Team in University(PCSIRT)(No.IRT13097)
文摘This paper introduces the canonical coordinates method to obtain the first integral of a single-degree freedom constraint mechanical system that contains conserva-tive and non-conservative constraint homonomic systems. The definition and properties of canonical coordinates are introduced. The relation between Lie point symmetries and the canonical coordinates of the constraint mechanical system are expressed. By this re-lation, the canonical coordinates can be obtained. Properties of the canonical coordinates and the Lie symmetry theory are used to seek the first integrals of constraint mechanical system. Three examples are used to show applications of the results.
