Seismic ray tracing in anisotropic media with irregular surface is crucial for the exploration of the fine crustal structure. Elliptically anisotropic medium is the type of anisotropic media with only four independent...Seismic ray tracing in anisotropic media with irregular surface is crucial for the exploration of the fine crustal structure. Elliptically anisotropic medium is the type of anisotropic media with only four independent elastic parameters. Usually, this medium can be described by only the vertical phase velocity and the horizontal phase velocity for seismic wave propagation. Model parameteri- zation in this study is described by flexible triangular grids, which is beneficial for the description of irregular surface with high degree of approximation. Both the vertical and horizontal phase velocities are defined in the triangular grids, respectively, which are used for the description of phase velocity distribution everywhere in the model by linear interpolation. We develop a shooting ray tracing method of turning wave in the elliptically anisotropic media with irregular surface. Runge-Kutta method is applied to solve the partial differential equation of seismic ray in elliptically anisotropic media. Linearly modified method is used for adjusting emergent phase angles in the shooting scheme. Numerical tests demonstrate that ray paths coincide well with analytical trajectories in trans- versely homogeneous elliptically anisotropic media. Seis- mic ray tracing results in transversely inhomogeneous elliptically anisotropic media demonstrate that our method is effective for further first-arrival tomography in ellipti- cally anisotropic media with an irregular surface.展开更多
Combining the linear transformation and the solution technique for the cubic equation, a general closed-form analytic solution for bulk waves in orthotropic anisotropic materials is obtained. This method is straightfo...Combining the linear transformation and the solution technique for the cubic equation, a general closed-form analytic solution for bulk waves in orthotropic anisotropic materials is obtained. This method is straightforward and general. Degenerated cases include transversely isotropic, cubic, and isotropic materials. Numerical computations are carried out on a fiber-reinforced composite plate modeled as a transversely isotropic media. The fibers are parallel to the top and bottom surfaces of the plate, and they are rotated counterclockwise around the plate normal through different angles. The two-dimensional slowness curves corresponding to different rotations are presented graphically. The wave propagation characteristics displayed in slowness surfaces for different fiber orientation are analyzed. Key words composite material - anisotropic media - wave propagation - slowness PASC 2001 0343.8 - 042 Project supported by the Science Foundation of Shanghai Municipal Commission of Education (Grant No. 03AK48)展开更多
The paper presents a staggered-grid any even-order accurate finite-difference scheme for two-dimensional (2D), three-component (3C), first-order stress-velocity elastic wave equation and its stability condition in the...The paper presents a staggered-grid any even-order accurate finite-difference scheme for two-dimensional (2D), three-component (3C), first-order stress-velocity elastic wave equation and its stability condition in the arbitrary tilt anisotropic media; and derives a perfectly matched absorbing layer (PML) boundary condition and its stag- gered-grid any even-order accurate difference scheme in the 2D arbitrary tilt anisotropic media. The results of nu- merical modeling indicate that the modeling precision is high, the calculation efficiency is satisfactory and the absorbing boundary condition is better. The wave-front shapes of elastic waves are complex in the anisotropic media, and the velocity of qP wave is not always faster than that of qS wave. The wave-front triplication of qS wave and its events in both reflected domain and propagated domain, which are not commonly hyperbola, is a common phenomenon. When the symmetry axis is tilted in the TI media, the phenomenon of S-wave splitting is clearly observed in the snaps of three components and synthetic seismograms, and the events of all kinds of waves are asymmetric.展开更多
Based on Biot theory of two-phase anisotropic media and Hamilton theory about dynamic problem,finite element equations of elastic wave propagation in two-phase anisotropic media are derived in this paper.Numerical sol...Based on Biot theory of two-phase anisotropic media and Hamilton theory about dynamic problem,finite element equations of elastic wave propagation in two-phase anisotropic media are derived in this paper.Numerical solution of finite element equations is given.Finally,Properties of elastic wave propagation are observed and analyzed through FEM modeling.展开更多
Static electromagnetic fields are studied based on standard spaces of the physical presentation, and the modal equations of static electromagnetic fields for anisotropic media are derived. By introducing a new set of ...Static electromagnetic fields are studied based on standard spaces of the physical presentation, and the modal equations of static electromagnetic fields for anisotropic media are derived. By introducing a new set of first-order potential functions, several novel theoretical results are obtained. It is found that, for isotropic media, electric or magnetic potentials are scalar; while for anisotropic media, they are vectors. Magnitude and direction of the vector potentials are related to the anisotropic subspaces. Based on these results, we discuss the laws of static electromagnetic fields for anisotropic media.展开更多
The scattering behavior of an anisotropic acoustic medium is analyzed to reveal the possibility of routing acoustic signals through the anisotropic layers with no backscattering loss. The sound-transparent effect of s...The scattering behavior of an anisotropic acoustic medium is analyzed to reveal the possibility of routing acoustic signals through the anisotropic layers with no backscattering loss. The sound-transparent effect of such a medium is achieved by independently modulating the anisotropic effective acoustic parameters in a specific order, and is experimentally observed in a bending waveguide by arranging the subwavelength structures in the bending part according to transformation acoustics. With the properly designed filling structures, the original distorted acoustic field in the bending waveguide is restored as if the wave travels along a straight path. The transmitted acoustic signal is maintained nearly the same as the incident modulated Gaussian pulse. The proposed schemes and the supporting results could be instructive for further acoustic manipulations such as wave steering, cloaking and beam splitting.展开更多
The purpose of this paper is to use the conforma mapping method[1]to analyzeand evaluate the ground displacement and scattering of incident SH-waves, on thesurface of semi-canyon topography of arbitrary shape with li...The purpose of this paper is to use the conforma mapping method[1]to analyzeand evaluate the ground displacement and scattering of incident SH-waves, on thesurface of semi-canyon topography of arbitrary shape with lining in anisotropic media.The problem to be solved can be reduced to the solution of an infinite algebraicequation set by using the method of full-space expansion of Fourier progression Usingthe mapping function and scattering theory to solve problems due to semi-canyon topography with lining is just like mapping the semi-cylindrical canyon of arbitraryshape into a cylindrical canyon in full-space.Moreover,it is far practical inengineering practice.From the computational examples,it is obvious that the variation of displacement amplitudes on the surface near the canyon topography is rather sharp. especially when the freqencies of incident SH-waves increase.展开更多
P-and S-wave separation plays an important role in elastic reverse-time migration.It can reduce the artifacts caused by crosstalk between different modes and improve image quality.In addition,P-and Swave separation ca...P-and S-wave separation plays an important role in elastic reverse-time migration.It can reduce the artifacts caused by crosstalk between different modes and improve image quality.In addition,P-and Swave separation can also be used to better understand and distinguish wave types in complex media.At present,the methods for separating wave modes in anisotropic media mainly include spatial nonstationary filtering,low-rank approximation,and vector Poisson equation.Most of these methods require multiple Fourier transforms or the calculation of large matrices,which require high computational costs for problems with large scale.In this paper,an efficient method is proposed to separate the wave mode for anisotropic media by using a scalar anisotropic Poisson operator in the spatial domain.For 2D problems,the computational complexity required by this method is 1/2 of the methods based on solving a vector Poisson equation.Therefore,compared with existing methods based on pseudoHelmholtz decomposition operators,this method can significantly reduce the computational cost.Numerical examples also show that the P and S waves decomposed by this method not only have the correct amplitude and phase relative to the input wavefield but also can reduce the computational complexity significantly.展开更多
A recursive algorithm is adopted for the computation of dyadic Green's functions in three-dimensional stratified uniaxial anisotropic media with arbitrary number of layers. Three linear equation groups for computing ...A recursive algorithm is adopted for the computation of dyadic Green's functions in three-dimensional stratified uniaxial anisotropic media with arbitrary number of layers. Three linear equation groups for computing the coefficients of the Sommerfeld integrals are obtained according to the continuity condition of electric and magnetic fields across the interface between different layers, which are in correspondence with the TM wave produced by a vertical unit electric dipole and the TE or TM wave produced by a horizontal unit electric dipole, respectively. All the linear equation groups can be solved via the recursive algorithm. The dyadic Green's functions with source point and field point being in any layer can be conveniently obtained by merely changing the position of the elements within the source term of the linear equation groups. The problem of singularities occurring in the Sommerfeld integrals is efficiently solved by deforming the integration path in the complex plane. The expression of the dyadic Green's functions provided by this paper is terse in form and is easy to be programmed, and it does not overflow. Theoretical analysis and numerical examples show the accuracy and effectivity of the algorithm.展开更多
This paper presents a new numerical technique for solving initial and bound-ary value problems with unsteady strongly nonlinear advection diffusion reaction(ADR)equations.The method is based on the use of the radial b...This paper presents a new numerical technique for solving initial and bound-ary value problems with unsteady strongly nonlinear advection diffusion reaction(ADR)equations.The method is based on the use of the radial basis functions(RBF)for the approximation space of the solution.The Crank-Nicolson scheme is used for approximation in time.This results in a sequence of stationary nonlinear ADR equations.The equations are solved sequentially at each time step using the proposed semi-analytical technique based on the RBFs.The approximate solution is sought in the form of the analytical expansion over basis functions and contains free parameters.The basis functions are constructed in such a way that the expansion satisfies the boundary conditions of the problem for any choice of the free parameters.The free parameters are determined by substitution of the expansion in the equation and collocation in the solution domain.In the case of a nonlinear equation,we use the well-known procedure of quasilinearization.This transforms the original equation into a sequence of the linear ones on each time layer.The numerical examples confirm the high accuracy and robustness of the proposed numerical scheme.展开更多
This is an expand of the complex function method in solving the problem of interaction of plane.SH-waves and non-circular cavity surfaced with linig in anisotropic media.the use the method similar to that incorporated...This is an expand of the complex function method in solving the problem of interaction of plane.SH-waves and non-circular cavity surfaced with linig in anisotropic media.the use the method similar to that incorporated in [2] added with Savin's method for solving stress concentration of non-circular cavity surfaced with lining in elasticity.Anisotropic media can be used ic simulate the conditions of thegeology.The solving proceeding for this problem can be processed conveniently in the manner similar to that introduced in [2].In this paper.as illustrated in example numerical studies have been done for a square cavity surfaced with lining in anisotropic media.展开更多
Simulation of elastic wave propagation has important applications in many areas such as inverse problemand geophysical exploration.In this paper,stability conditions for wave simulation in 3-D anisotropic media with t...Simulation of elastic wave propagation has important applications in many areas such as inverse problemand geophysical exploration.In this paper,stability conditions for wave simulation in 3-D anisotropic media with the pseudospectral method are investigated.They can be expressed explicitly by elasticity constants which are easy to be applied in computations.The 3-Dwave simulation for two typical anisotropic media,transversely isotropic media and orthorhombic media,are carried out.The results demonstrate some satisfactory behaviors of the pseudospectral method.展开更多
The method of reverberation-ray matrix (MRRM) is extended and modified for the analysis of free wave propagation in anisotropic layered elastic media. A general, numerically stable formulation is established within ...The method of reverberation-ray matrix (MRRM) is extended and modified for the analysis of free wave propagation in anisotropic layered elastic media. A general, numerically stable formulation is established within the state space framework. The compatibility of physical variables in local dual coordinates gives the phase relation, from which exponentially growing functions are excluded. The interface and boundary conditions lead to the scattering relation, which avoids matrix inversion operation. Numerical examples are given to show the high accuracy of the present MRRM.展开更多
Basedonthe first-order Biot-equation with simplified coefficients,astaggered irregu- lar-grid finite difference method(FDM)is developed to simulate elastic wave propagation in 3-D heterogeneous anisotropic porous medi...Basedonthe first-order Biot-equation with simplified coefficients,astaggered irregu- lar-grid finite difference method(FDM)is developed to simulate elastic wave propagation in 3-D heterogeneous anisotropic porous media.The ‘slow’P wave in porous media wave simulation is highly dispersive.Finer grids are needed to get a precise wavefield calculation for models with curved interface and complex geometric structure.Fine grids in a global model greatly increase computation costs of regular grids scheme.Irregular fine or coarse grids in local fields not only cost less computing time than the conventional velocity-stress FDM,but also give a more accu- rate wavefield description.A dispersion analysis of the irregular-grid finite difference operator has confirmed the stability and high efficiency.The absorbing boundary condition is used to elimi- nate artificial reflections.Numerical examples show that this new irregular-grid finite difference method is of higher performance than conventional methods using regular rectangular grids in simulating elastic wave propagation in heterogeneous anisotropic porous media.展开更多
Based on angular spectrum expansion and 4 × 4 matrix theory, the reflection and transmission characteristics of a Laguerre Gaussian (LG) beam from uniaxial anisotropic multilayered media are studied. The reflec...Based on angular spectrum expansion and 4 × 4 matrix theory, the reflection and transmission characteristics of a Laguerre Gaussian (LG) beam from uniaxial anisotropic multilayered media are studied. The reflected and transmitted beam fields of an LG beam are derived. In the case where the principal coordinates of the uniaxial anisotropic media coincide with the global coordinates, the reflected and transmitted beam intensities from a uniaxial anisotropic slab and three-layered media are numerically simulated. It is shown that the reflected intensity components of the incident beam, especially the TM polarized incident beam, are smaller than the transmitted intensity components. The distortion of the reflected intensity component is more evident than that of the transmitted intensity component. The distortion of intensity distribution is greatly affected by the dielectric tensor and the thickness of anisotropic media. We finally extend the application of the method to general anisotropic multilayered media.展开更多
The problem of a Griffith crack in an unbounded orthotropic functionally graded material subjected to antipole shear impact was studied. The shear moduli in two directions of the functionally graded material were assu...The problem of a Griffith crack in an unbounded orthotropic functionally graded material subjected to antipole shear impact was studied. The shear moduli in two directions of the functionally graded material were assumed to vary proportionately as definite gradient. By using integral transforms and dual integral equations, the local dynamic stress field was obtained. The results of dynamic stress intensity factor show that increasing shear moduli's gradient of FGM or increasing the shear modulus in direction perpendicular to crack surface can restrain the magnitude of dynamic stress intensity factor.展开更多
Elliptic vortex solitons are investigated in anisotropic nonlocal media with more general formulations. We ad- dress the existence and dynamics of such solitons analytically and numerically. The solution of elliptic v...Elliptic vortex solitons are investigated in anisotropic nonlocal media with more general formulations. We ad- dress the existence and dynamics of such solitons analytically and numerically. The solution of elliptic vortex solitons depends on the eccentricity of both the input beam and nonlocal response function. With different degrees of nonlocality, we numerically investigate the evolution of the elliptic vortex solitons, and find that, typically, the elliptic vortex solitons with single and double charges collapse into spiraling dipole- and tripole- like soliton clusters, respectively.展开更多
The conductivity anisotropy behaviour is described for certain environment in the Earths crust and the MT inversion method for a layered symmetrically anisotropic model is presented. The inversion interpretations of t...The conductivity anisotropy behaviour is described for certain environment in the Earths crust and the MT inversion method for a layered symmetrically anisotropic model is presented. The inversion interpretations of the anisotropic model from the observational data are helpful to identify the earthquake precusors as indicated by the deep conductivity anisotropic variations, and also provide some useful information to investigate the stress states and deformation bands in the deep crust of the Earth.展开更多
In this paper, we present a discrete duality finite volume (DDFV) method for 2-D flow problems in nonhomogeneous anisotropic porous media under diverse boundary conditions. We use the discrete gradient defined in diam...In this paper, we present a discrete duality finite volume (DDFV) method for 2-D flow problems in nonhomogeneous anisotropic porous media under diverse boundary conditions. We use the discrete gradient defined in diamond cells to compute the fluxes. We focus on the case of Dirichlet, full Neumann and periodic boundary conditions. Taking into account the periodicity is the main new ingredient with respect to our recent works. We explain the procedures step by step, for numerical solutions. We develop a matlab code for algebraic equations. Numerical tests were provided to confirm our theoretical results.展开更多
A modified Fourier's law in an anisotropic and non-homogeneous media results in a heat equation with memory, for which the memory kernel is matrix-valued and spatially dependent. Different conditions on the memory ke...A modified Fourier's law in an anisotropic and non-homogeneous media results in a heat equation with memory, for which the memory kernel is matrix-valued and spatially dependent. Different conditions on the memory kernel lead to the equation being either a parabolic type or a hyperbolic type. Well-posedness of such a heat equation is established under some general and reasonable conditions. It is shown that the propagation speed for heat pulses could be either infinite or finite, depending on the different types of the memory kernels. Our analysis indicates that, in the framework of linear theory, heat equation with hyperbolic kernel is a more realistic model for the heat conduction, which might be of some interest in physics.展开更多
基金financial support for this work contributed by the National Key Research and Development Program of China(Grants Nos.2016YFC0600101,2016YFC0600201 and 2016YFC0600302)the National Natural Science Foundation of China(Grants Nos.41522401 and 41474068)
文摘Seismic ray tracing in anisotropic media with irregular surface is crucial for the exploration of the fine crustal structure. Elliptically anisotropic medium is the type of anisotropic media with only four independent elastic parameters. Usually, this medium can be described by only the vertical phase velocity and the horizontal phase velocity for seismic wave propagation. Model parameteri- zation in this study is described by flexible triangular grids, which is beneficial for the description of irregular surface with high degree of approximation. Both the vertical and horizontal phase velocities are defined in the triangular grids, respectively, which are used for the description of phase velocity distribution everywhere in the model by linear interpolation. We develop a shooting ray tracing method of turning wave in the elliptically anisotropic media with irregular surface. Runge-Kutta method is applied to solve the partial differential equation of seismic ray in elliptically anisotropic media. Linearly modified method is used for adjusting emergent phase angles in the shooting scheme. Numerical tests demonstrate that ray paths coincide well with analytical trajectories in trans- versely homogeneous elliptically anisotropic media. Seis- mic ray tracing results in transversely inhomogeneous elliptically anisotropic media demonstrate that our method is effective for further first-arrival tomography in ellipti- cally anisotropic media with an irregular surface.
文摘Combining the linear transformation and the solution technique for the cubic equation, a general closed-form analytic solution for bulk waves in orthotropic anisotropic materials is obtained. This method is straightforward and general. Degenerated cases include transversely isotropic, cubic, and isotropic materials. Numerical computations are carried out on a fiber-reinforced composite plate modeled as a transversely isotropic media. The fibers are parallel to the top and bottom surfaces of the plate, and they are rotated counterclockwise around the plate normal through different angles. The two-dimensional slowness curves corresponding to different rotations are presented graphically. The wave propagation characteristics displayed in slowness surfaces for different fiber orientation are analyzed. Key words composite material - anisotropic media - wave propagation - slowness PASC 2001 0343.8 - 042 Project supported by the Science Foundation of Shanghai Municipal Commission of Education (Grant No. 03AK48)
基金Fund Project of Key Lab of Geophysical Exploration of China National Petroleum Corporation (GPR0408).
文摘The paper presents a staggered-grid any even-order accurate finite-difference scheme for two-dimensional (2D), three-component (3C), first-order stress-velocity elastic wave equation and its stability condition in the arbitrary tilt anisotropic media; and derives a perfectly matched absorbing layer (PML) boundary condition and its stag- gered-grid any even-order accurate difference scheme in the 2D arbitrary tilt anisotropic media. The results of nu- merical modeling indicate that the modeling precision is high, the calculation efficiency is satisfactory and the absorbing boundary condition is better. The wave-front shapes of elastic waves are complex in the anisotropic media, and the velocity of qP wave is not always faster than that of qS wave. The wave-front triplication of qS wave and its events in both reflected domain and propagated domain, which are not commonly hyperbola, is a common phenomenon. When the symmetry axis is tilted in the TI media, the phenomenon of S-wave splitting is clearly observed in the snaps of three components and synthetic seismograms, and the events of all kinds of waves are asymmetric.
文摘Based on Biot theory of two-phase anisotropic media and Hamilton theory about dynamic problem,finite element equations of elastic wave propagation in two-phase anisotropic media are derived in this paper.Numerical solution of finite element equations is given.Finally,Properties of elastic wave propagation are observed and analyzed through FEM modeling.
基金supported by the National Natural Science Foundation of China (No.50778179)
文摘Static electromagnetic fields are studied based on standard spaces of the physical presentation, and the modal equations of static electromagnetic fields for anisotropic media are derived. By introducing a new set of first-order potential functions, several novel theoretical results are obtained. It is found that, for isotropic media, electric or magnetic potentials are scalar; while for anisotropic media, they are vectors. Magnitude and direction of the vector potentials are related to the anisotropic subspaces. Based on these results, we discuss the laws of static electromagnetic fields for anisotropic media.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11974186,11604153,and 61975080)the Natural Science Foundation of Jiangsu Province,China(Grant Nos.BK20160818 and BK20200070)the Open Research Foundation of Key Laboratory of Modern Acoustics,Ministry of Education。
文摘The scattering behavior of an anisotropic acoustic medium is analyzed to reveal the possibility of routing acoustic signals through the anisotropic layers with no backscattering loss. The sound-transparent effect of such a medium is achieved by independently modulating the anisotropic effective acoustic parameters in a specific order, and is experimentally observed in a bending waveguide by arranging the subwavelength structures in the bending part according to transformation acoustics. With the properly designed filling structures, the original distorted acoustic field in the bending waveguide is restored as if the wave travels along a straight path. The transmitted acoustic signal is maintained nearly the same as the incident modulated Gaussian pulse. The proposed schemes and the supporting results could be instructive for further acoustic manipulations such as wave steering, cloaking and beam splitting.
文摘The purpose of this paper is to use the conforma mapping method[1]to analyzeand evaluate the ground displacement and scattering of incident SH-waves, on thesurface of semi-canyon topography of arbitrary shape with lining in anisotropic media.The problem to be solved can be reduced to the solution of an infinite algebraicequation set by using the method of full-space expansion of Fourier progression Usingthe mapping function and scattering theory to solve problems due to semi-canyon topography with lining is just like mapping the semi-cylindrical canyon of arbitraryshape into a cylindrical canyon in full-space.Moreover,it is far practical inengineering practice.From the computational examples,it is obvious that the variation of displacement amplitudes on the surface near the canyon topography is rather sharp. especially when the freqencies of incident SH-waves increase.
基金supported by the National Key R&D Program of China(No.2018YFA0702505)the project of CNOOC Limited(Grant No.CNOOC-KJ GJHXJSGG YF 2022-01)+1 种基金R&D Department of China National Petroleum Corporation(Investigations on fundamental experiments and advanced theoretical methods in geophysical prospecting application,2022DQ0604-02)NSFC(Grant Nos.U23B20159,41974142,42074129,12001311)。
文摘P-and S-wave separation plays an important role in elastic reverse-time migration.It can reduce the artifacts caused by crosstalk between different modes and improve image quality.In addition,P-and Swave separation can also be used to better understand and distinguish wave types in complex media.At present,the methods for separating wave modes in anisotropic media mainly include spatial nonstationary filtering,low-rank approximation,and vector Poisson equation.Most of these methods require multiple Fourier transforms or the calculation of large matrices,which require high computational costs for problems with large scale.In this paper,an efficient method is proposed to separate the wave mode for anisotropic media by using a scalar anisotropic Poisson operator in the spatial domain.For 2D problems,the computational complexity required by this method is 1/2 of the methods based on solving a vector Poisson equation.Therefore,compared with existing methods based on pseudoHelmholtz decomposition operators,this method can significantly reduce the computational cost.Numerical examples also show that the P and S waves decomposed by this method not only have the correct amplitude and phase relative to the input wavefield but also can reduce the computational complexity significantly.
文摘A recursive algorithm is adopted for the computation of dyadic Green's functions in three-dimensional stratified uniaxial anisotropic media with arbitrary number of layers. Three linear equation groups for computing the coefficients of the Sommerfeld integrals are obtained according to the continuity condition of electric and magnetic fields across the interface between different layers, which are in correspondence with the TM wave produced by a vertical unit electric dipole and the TE or TM wave produced by a horizontal unit electric dipole, respectively. All the linear equation groups can be solved via the recursive algorithm. The dyadic Green's functions with source point and field point being in any layer can be conveniently obtained by merely changing the position of the elements within the source term of the linear equation groups. The problem of singularities occurring in the Sommerfeld integrals is efficiently solved by deforming the integration path in the complex plane. The expression of the dyadic Green's functions provided by this paper is terse in form and is easy to be programmed, and it does not overflow. Theoretical analysis and numerical examples show the accuracy and effectivity of the algorithm.
基金supported by the Fundamental Research Funds for the Central Universities(No.2018B16714)the National Natural Science Foundation of China(Nos.11702083,11572111,51679150,51579153,51739008,51527811)+5 种基金the State Key Laboratory of Mechanics and Control of Mechanical Structures(Nanjing University of Aeronautics and Astronautics)(No.MCMS-0218G01)the China Postdoctoral Science Foundation(No.2017M611669)the China Postdoctoral Science Special Foundation(No.2018T110430)the Postdoctoral Foundation of Jiangsu Province(No.1701059C)the National Key R&D Program of China(No.2016YFC0401902)the Fund Project of NHRI(Nos.Y417002,Y417015).
文摘This paper presents a new numerical technique for solving initial and bound-ary value problems with unsteady strongly nonlinear advection diffusion reaction(ADR)equations.The method is based on the use of the radial basis functions(RBF)for the approximation space of the solution.The Crank-Nicolson scheme is used for approximation in time.This results in a sequence of stationary nonlinear ADR equations.The equations are solved sequentially at each time step using the proposed semi-analytical technique based on the RBFs.The approximate solution is sought in the form of the analytical expansion over basis functions and contains free parameters.The basis functions are constructed in such a way that the expansion satisfies the boundary conditions of the problem for any choice of the free parameters.The free parameters are determined by substitution of the expansion in the equation and collocation in the solution domain.In the case of a nonlinear equation,we use the well-known procedure of quasilinearization.This transforms the original equation into a sequence of the linear ones on each time layer.The numerical examples confirm the high accuracy and robustness of the proposed numerical scheme.
文摘This is an expand of the complex function method in solving the problem of interaction of plane.SH-waves and non-circular cavity surfaced with linig in anisotropic media.the use the method similar to that incorporated in [2] added with Savin's method for solving stress concentration of non-circular cavity surfaced with lining in elasticity.Anisotropic media can be used ic simulate the conditions of thegeology.The solving proceeding for this problem can be processed conveniently in the manner similar to that introduced in [2].In this paper.as illustrated in example numerical studies have been done for a square cavity surfaced with lining in anisotropic media.
基金supported by the 973 State Key Project under the grant No.2010 CB731505supported by the key national natural science foundation of China under the grant No.10431030the Chair foundation of State Key Laboratory of Scientific and Engineering Computing(LSEC).
文摘Simulation of elastic wave propagation has important applications in many areas such as inverse problemand geophysical exploration.In this paper,stability conditions for wave simulation in 3-D anisotropic media with the pseudospectral method are investigated.They can be expressed explicitly by elasticity constants which are easy to be applied in computations.The 3-Dwave simulation for two typical anisotropic media,transversely isotropic media and orthorhombic media,are carried out.The results demonstrate some satisfactory behaviors of the pseudospectral method.
基金supported by the National Natural Science Foundation of China(Nos.10725210,10832009 and 10432030)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20060335107)the Program for New Century Excellent Talents in University(No.NCET-05-05010).
文摘The method of reverberation-ray matrix (MRRM) is extended and modified for the analysis of free wave propagation in anisotropic layered elastic media. A general, numerically stable formulation is established within the state space framework. The compatibility of physical variables in local dual coordinates gives the phase relation, from which exponentially growing functions are excluded. The interface and boundary conditions lead to the scattering relation, which avoids matrix inversion operation. Numerical examples are given to show the high accuracy of the present MRRM.
文摘Basedonthe first-order Biot-equation with simplified coefficients,astaggered irregu- lar-grid finite difference method(FDM)is developed to simulate elastic wave propagation in 3-D heterogeneous anisotropic porous media.The ‘slow’P wave in porous media wave simulation is highly dispersive.Finer grids are needed to get a precise wavefield calculation for models with curved interface and complex geometric structure.Fine grids in a global model greatly increase computation costs of regular grids scheme.Irregular fine or coarse grids in local fields not only cost less computing time than the conventional velocity-stress FDM,but also give a more accu- rate wavefield description.A dispersion analysis of the irregular-grid finite difference operator has confirmed the stability and high efficiency.The absorbing boundary condition is used to elimi- nate artificial reflections.Numerical examples show that this new irregular-grid finite difference method is of higher performance than conventional methods using regular rectangular grids in simulating elastic wave propagation in heterogeneous anisotropic porous media.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61475123,61571355,and 61308025)the Natural Science Basic Research Plan in Shaanxi Province,China(Grant No.2016JQ4015)the Overseas Training Program for Young Backbones Teachers Sponsored by China Scholarship Council and Xidian University
文摘Based on angular spectrum expansion and 4 × 4 matrix theory, the reflection and transmission characteristics of a Laguerre Gaussian (LG) beam from uniaxial anisotropic multilayered media are studied. The reflected and transmitted beam fields of an LG beam are derived. In the case where the principal coordinates of the uniaxial anisotropic media coincide with the global coordinates, the reflected and transmitted beam intensities from a uniaxial anisotropic slab and three-layered media are numerically simulated. It is shown that the reflected intensity components of the incident beam, especially the TM polarized incident beam, are smaller than the transmitted intensity components. The distortion of the reflected intensity component is more evident than that of the transmitted intensity component. The distortion of intensity distribution is greatly affected by the dielectric tensor and the thickness of anisotropic media. We finally extend the application of the method to general anisotropic multilayered media.
文摘The problem of a Griffith crack in an unbounded orthotropic functionally graded material subjected to antipole shear impact was studied. The shear moduli in two directions of the functionally graded material were assumed to vary proportionately as definite gradient. By using integral transforms and dual integral equations, the local dynamic stress field was obtained. The results of dynamic stress intensity factor show that increasing shear moduli's gradient of FGM or increasing the shear modulus in direction perpendicular to crack surface can restrain the magnitude of dynamic stress intensity factor.
基金supported in part by the National Natural Science Foundation of China(Nos.11347180 and 11347136)the Natural Science Foundation of Jiangsu Province(No.BK20130265)+1 种基金the Research Fund of Suzhou University of Science and Technology(No.XKQ201210)the Innovation Program of Shanghai Municipal Education Commission
文摘Elliptic vortex solitons are investigated in anisotropic nonlocal media with more general formulations. We ad- dress the existence and dynamics of such solitons analytically and numerically. The solution of elliptic vortex solitons depends on the eccentricity of both the input beam and nonlocal response function. With different degrees of nonlocality, we numerically investigate the evolution of the elliptic vortex solitons, and find that, typically, the elliptic vortex solitons with single and double charges collapse into spiraling dipole- and tripole- like soliton clusters, respectively.
文摘The conductivity anisotropy behaviour is described for certain environment in the Earths crust and the MT inversion method for a layered symmetrically anisotropic model is presented. The inversion interpretations of the anisotropic model from the observational data are helpful to identify the earthquake precusors as indicated by the deep conductivity anisotropic variations, and also provide some useful information to investigate the stress states and deformation bands in the deep crust of the Earth.
文摘In this paper, we present a discrete duality finite volume (DDFV) method for 2-D flow problems in nonhomogeneous anisotropic porous media under diverse boundary conditions. We use the discrete gradient defined in diamond cells to compute the fluxes. We focus on the case of Dirichlet, full Neumann and periodic boundary conditions. Taking into account the periodicity is the main new ingredient with respect to our recent works. We explain the procedures step by step, for numerical solutions. We develop a matlab code for algebraic equations. Numerical tests were provided to confirm our theoretical results.
基金Supported by National Natural Science Foundation of China under grants 10831007, 60821091 and 60974035, National Basic Research Program of China (973 Program) under grant 2011CB808002, and the project MTM2008- 03541 of the Spanish Ministry of Science and Innovation
文摘A modified Fourier's law in an anisotropic and non-homogeneous media results in a heat equation with memory, for which the memory kernel is matrix-valued and spatially dependent. Different conditions on the memory kernel lead to the equation being either a parabolic type or a hyperbolic type. Well-posedness of such a heat equation is established under some general and reasonable conditions. It is shown that the propagation speed for heat pulses could be either infinite or finite, depending on the different types of the memory kernels. Our analysis indicates that, in the framework of linear theory, heat equation with hyperbolic kernel is a more realistic model for the heat conduction, which might be of some interest in physics.