3D eikonal equation is a partial differential equation for the calculation of first-arrival traveltimes and has been widely applied in many scopes such as ray tracing,source localization,reflection migration,seismic m...3D eikonal equation is a partial differential equation for the calculation of first-arrival traveltimes and has been widely applied in many scopes such as ray tracing,source localization,reflection migration,seismic monitoring and tomographic imaging.In recent years,many advanced methods have been developed to solve the 3D eikonal equation in heterogeneous media.However,there are still challenges for the stable and accurate calculation of first-arrival traveltimes in 3D strongly inhomogeneous media.In this paper,we propose an adaptive finite-difference(AFD)method to numerically solve the 3D eikonal equation.The novel method makes full use of the advantages of different local operators characterizing different seismic wave types to calculate factors and traveltimes,and then the most accurate factor and traveltime are adaptively selected for the convergent updating based on the Fermat principle.Combined with global fast sweeping describing seismic waves propagating along eight directions in 3D media,our novel method can achieve the robust calculation of first-arrival traveltimes with high precision at grid points either near source point or far away from source point even in a velocity model with large and sharp contrasts.Several numerical examples show the good performance of the AFD method,which will be beneficial to many scientific applications.展开更多
Several new concepts of enhanced pullback attractors for nonautonomous dynamical systems are introduced here by uniformly enhancing the compactness and attraction of the usual pullback attractors over an infinite forw...Several new concepts of enhanced pullback attractors for nonautonomous dynamical systems are introduced here by uniformly enhancing the compactness and attraction of the usual pullback attractors over an infinite forward time-interval under strong and weak topologies.Then we provide some theoretical results for the existence,regularity and asymptotic stability of these enhanced pullback attractors under general theoretical frameworks which can be applied to a large class of PDEs.The existence of these enhanced attractors is harder to obtain than the backward case[33],since it is difficult to uniformly control the long-time pullback behavior of the systems over the forward time-interval.As applications of our theoretical results,we consider the famous 3D primitive equations modelling the large-scale ocean and atmosphere dynamics,and prove the existence,regularity and asymptotic stability of the enhanced pullback attractors in V×V and H^(2)×H^(2) for the time-dependent forces which satisfy some weak conditions.展开更多
A theoretical model is developed for predicting both conduction and diffusion in thin-film ionic conductors or cables. With the linearized Poisson-Nernst-Planck(PNP)theory, the two-dimensional(2D) equations for thin i...A theoretical model is developed for predicting both conduction and diffusion in thin-film ionic conductors or cables. With the linearized Poisson-Nernst-Planck(PNP)theory, the two-dimensional(2D) equations for thin ionic conductor films are obtained from the three-dimensional(3D) equations by power series expansions in the film thickness coordinate, retaining the lower-order equations. The thin-film equations for ionic conductors are combined with similar equations for one thin dielectric film to derive the 2D equations of thin sandwich films composed of a dielectric layer and two ionic conductor layers. A sandwich film in the literature, as an ionic cable, is analyzed as an example of the equations obtained in this paper. The numerical results show the effect of diffusion in addition to the conduction treated in the literature. The obtained theoretical model including both conduction and diffusion phenomena can be used to investigate the performance of ionic-conductor devices with any frequency.展开更多
As one of the most important ways to reduce the greenhouse gas emission,carbon dioxide(CO2)enhanced gas recovery(CO2-EGR) is attractive since the gas recovery can be enhanced simultaneously with CO2sequestration.B...As one of the most important ways to reduce the greenhouse gas emission,carbon dioxide(CO2)enhanced gas recovery(CO2-EGR) is attractive since the gas recovery can be enhanced simultaneously with CO2sequestration.Based on the existing equation of state(EOS) module of TOUGH2 MP,extEOS7C is developed to calculate the phase partition of H2O-CO2-CH4-NaCl mixtures accurately with consideration of dissolved NaCI and brine properties at high pressure and temperature conditions.Verifications show that it can be applied up to the pressure of 100 MPa and temperature of 150℃.The module was implemented in the linked simulator TOUGH2MP-FLAC3 D for the coupled hydro-mechanical simulations.A simplified three-dimensional(3D)1/4 model(2.2 km×1 km×1 km) which consists of the whole reservoir,caprock and baserock was generated based on the geological conditions of a gas field in the North German Basin.The simulation results show that,under an injection rate of 200,000 t/yr and production rate of 200,000 sm3/d,CO2breakthrough occurred in the case with the initial reservoir pressure of 5 MPa but did not occur in the case of 42 MPa.Under low pressure conditions,the pressure driven horizontal transport is the dominant process;while under high pressure conditions,the density driven vertical flow is dominant.Under the considered conditions,the CO2-EGR caused only small pressure changes.The largest pore pressure increase(2 MPa) and uplift(7 mm) occurred at the caprock bottom induced by only CO2injection.The caprock had still the primary stress state and its integrity was not affected.The formation water salinity and temperature variations of ±20℃ had small influences on the CO2-EGR process.In order to slow down the breakthrough,it is suggested that CO2-EGR should be carried out before the reservoir pressure drops below the critical pressure of CO2.展开更多
This paper obtains Lagrange equations of nonholonomic systems with fractional derivatives. First, the exchanging relationships between the isochronous variation and the fractional derivatives are derived. Secondly, ba...This paper obtains Lagrange equations of nonholonomic systems with fractional derivatives. First, the exchanging relationships between the isochronous variation and the fractional derivatives are derived. Secondly, based on these exchanging relationships, the Hamilton's principle is presented for non-conservative systems with fractional derivatives. Thirdly, Lagrange equations of the systems are obtained. Furthermore, the d'Alembert-Lagrange principle with fractional derivatives is presented, and the Lagrange equations of nonholonomic systems with fractional derivatives are studied. An example is designed to illustrate these results.展开更多
In this paper,we proposal stream surface and stream layer.By using classical tensor calculus,we derive 3-D Navier-Stokes Equations(NSE)in the stream layer under semigeodesic coordinate system,Navier-Stokes equation on...In this paper,we proposal stream surface and stream layer.By using classical tensor calculus,we derive 3-D Navier-Stokes Equations(NSE)in the stream layer under semigeodesic coordinate system,Navier-Stokes equation on the stream surface and 2-D Navier-Stokes equations on a two dimensional manifold. After introducing stream function on the stream surface,a nonlinear initial-boundary value problem satisfies by stream function is obtained,existence and uniqueness of its solution are proven.Based this theory we proposal a new method called"dimension split method"to solve 3D NSE.展开更多
To further study the nal solitons on the continental fission laws of initial intershelf/slope, we rederive and correct the 2D KdV equation of Djordjevic & Redekopp for exponentially stratified fluid (or ocean) and ...To further study the nal solitons on the continental fission laws of initial intershelf/slope, we rederive and correct the 2D KdV equation of Djordjevic & Redekopp for exponentially stratified fluid (or ocean) and with twodimensional topography. Through a combination of theoretical study and numerical experiments, we show that solitons in the odd vertical modes can fission. However, because of the corrections, the fission conditions are different from those of Djordjevic & Redekopp. The even modes cannot fission unless the initial internal solitons propagate from shallow sea to deep sea. This conclusion is entirely opposite to that of Djordjevic & Redekopp.展开更多
A three-dimensional (3D) predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is ...A three-dimensional (3D) predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa- tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.展开更多
In this paper, an explicit method is generalized from 1D and 2D models to a 3D model for numerical simulation of wave motion, and the corresponding recursion formulas are developed for 3D irregular grids. For uniform ...In this paper, an explicit method is generalized from 1D and 2D models to a 3D model for numerical simulation of wave motion, and the corresponding recursion formulas are developed for 3D irregular grids. For uniform cubic grids, the approach used to establish stable formulas with 2M-order accuracy is discussed in detail, with M being a positive integer, and is illustrated by establishing second order (M=1) recursion formulas. The theoretical results presented in this paper are demonstrated through numerical testing.展开更多
The 2D generalized stochastic Ginzburg-Landau equation with additive noise is considered. The compactness of the random dynamical system is established with a priori estimate method, showing that the random dynamical ...The 2D generalized stochastic Ginzburg-Landau equation with additive noise is considered. The compactness of the random dynamical system is established with a priori estimate method, showing that the random dynamical system possesses a random attractor in H^1 0.展开更多
Two high-order splitting schemes based on the idea of the operators splitting method are given. The three-dimensional advection-diffusion equation was split into several one-dimensional equations that were solved by t...Two high-order splitting schemes based on the idea of the operators splitting method are given. The three-dimensional advection-diffusion equation was split into several one-dimensional equations that were solved by these two schemes, only three computational grid points were needed in each direction but the accuracy reaches the spatial fourth-order. The third scheme proposed is based on the classical ADI scheme and the accuracy of the advection term of it can reach the spatial fourth-order. Finally, two typical numerical experiments show that the solutions of these three schemes compare well with that given by the analytical solution when the Peclet number is not bigger than 5.展开更多
This paper describes formulation and implementation of the fast multipole boundary element method (FMBEM) for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the...This paper describes formulation and implementation of the fast multipole boundary element method (FMBEM) for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the FMBEM are described in details. They are moment calculation, moment to moment translation, moment to local translation, and local to local translation. A data structure for the quad-tree construction is proposed which can facilitate implementation. An analytical moment expression is derived, which is more accurate, stable, and efficient than direct numerical computation. Numerical examples are presented to demonstrate the accuracy and efficiency of the FMBEM, and radiation of a 2D vibration rail mode is simulated using the FMBEM.展开更多
Within the framework of continuum mechanics, the double power series ex- pansion technique is proposed, and a series of reduced one-dimensional (1D) equations for a piezoelectric semiconductor beam are obtained. The...Within the framework of continuum mechanics, the double power series ex- pansion technique is proposed, and a series of reduced one-dimensional (1D) equations for a piezoelectric semiconductor beam are obtained. These derived equations are universal, in which extension, flexure, and shear deformations are all included, and can be degen- erated to a number of special cases, e.g., extensional motion, coupled extensional and flexural motion with shear deformations, and elementary flexural motion without shear deformations. As a typical application, the extensional motion of a ZnO beam is analyzed sequentially. It is revealed that semi-conduction has a great effect on the performance of the piezoelectric semiconductor beam, including static deformations and dynamic be- haviors. A larger initial carrier density will evidently lead to a lower resonant frequency and a smaller displacement response, which is a little similar to the dissipative effect. Both the derived approximate equations and the corresponding qualitative analysis are general and widely applicable, which can clearly interpret the inner physical mechanism of the semiconductor in the piezoelectrics and provide theoretical guidance for further experimental design.展开更多
A new method for solving the 1D Poisson equation is presented using the finite difference method. This method is based on the exact formulation of the inverse of the tridiagonal matrix associated with the Laplacian. T...A new method for solving the 1D Poisson equation is presented using the finite difference method. This method is based on the exact formulation of the inverse of the tridiagonal matrix associated with the Laplacian. This is the first time that the inverse of this remarkable matrix is determined directly and exactly. Thus, solving 1D Poisson equation becomes very accurate and extremely fast. This method is a very important tool for physics and engineering where the Poisson equation appears very often in the description of certain phenomena.展开更多
In this paper we propose a numerical approach to solve the relativistic Dirac equation suitable for computational calculations of one-electron systems. A variational procedure is carried out similar to the well-known ...In this paper we propose a numerical approach to solve the relativistic Dirac equation suitable for computational calculations of one-electron systems. A variational procedure is carried out similar to the well-known Hylleraas computational method. An application of the method to hydrogen isoelectronic atoms is presented, showing its consistency and high accuracy, relative to the exact analytical eigenvalues.展开更多
We study the D-dimensional Schrodinger equation for an energy-dependent Hamiltonian that linearlydepends on energy and quadraticJy on the relative distance.Next,via the Nikiforov-Uvarov (NU) method,we calculatethe cor...We study the D-dimensional Schrodinger equation for an energy-dependent Hamiltonian that linearlydepends on energy and quadraticJy on the relative distance.Next,via the Nikiforov-Uvarov (NU) method,we calculatethe corresponding eigenfunctions and eigenvalues.展开更多
The Rayleigh-Ritz and the inverse iteration methods are used in order to compute the eigenvalues of 3D Fredholm-Stieltjes integral equations, i.e. 3D Fredholm equations with respect to suitable Stieltjes-type measures...The Rayleigh-Ritz and the inverse iteration methods are used in order to compute the eigenvalues of 3D Fredholm-Stieltjes integral equations, i.e. 3D Fredholm equations with respect to suitable Stieltjes-type measures. Some applications are shown, relevant to the problem of computing the eigenvalues of a body charged by a finite number of masses concentrated on points, curves or surfaces lying in.展开更多
DC Resistivity Tomography is a non-linear inversion problem. So far there are mainly two kinds of inversion methods, based on the finite-element method and alpha centers method. In this paper, the disadvantages of the...DC Resistivity Tomography is a non-linear inversion problem. So far there are mainly two kinds of inversion methods, based on the finite-element method and alpha centers method. In this paper, the disadvantages of these two kinds of methods were analysed,and a new method of forward modeling and inversion (Tomography) based on boundary integral equations was proposed. This scheme successfuly overcomes the difficulties of the two formarly methods. It isn’t necessary to use the linearization approximation and calculate the Jacobi matrix. Numerical modeling results given in this paper showed that the computation speed of our method is fast, and there is not any special requirement for initial model, and satisfying results of tomography can be obtained in the case of great contrast of conductivity. So it has wide applications.展开更多
A physically-based numerical three-dimensional earthen dam piping failure model is developed for homogeneous and zoned soil dams.This model is an erosion model,coupled with force/moment equilibrium analyses.Orifice fl...A physically-based numerical three-dimensional earthen dam piping failure model is developed for homogeneous and zoned soil dams.This model is an erosion model,coupled with force/moment equilibrium analyses.Orifice flow and two-dimensional(2D)shallow water equations(SWE)are solved to simulate dam break flows at different breaching stages.Erosion rates of different soils with different construction compaction efforts are calculated using corresponding erosion formulae.The dam's real shape,soil properties,and surrounding area are programmed.Large outer 2D-SWE grids are used to control upstream and downstream hydraulic conditions and control the boundary conditions of orifice flow,and inner 2D-SWE flow is used to scour soil and perform force/moment equilibrium analyses.This model is validated using the European Commission IMPACT(Investigation of Extreme Flood Processes and Uncertainty)Test#5 in Norway,Teton Dam failure in Idaho,USA,and Quail Creek Dike failure in Utah,USA.All calculated peak outflows are within 10%errors of observed values.Simulation results show that,for a V-shaped dam like Teton Dam,a piping breach location at the abutment tends to result in a smaller peak breach outflow than the piping breach location at the dam's center;and if Teton Dam had broken from its center for internal erosion,a peak outflow of 117851 m'/s,which is 81%larger than the peak outflow of 65120 m3/s released from its right abutment,would have been released from Teton Dam.A lower piping inlet elevation tends to cause a faster/earlier piping breach than a higher piping inlet elevation.展开更多
The fluid variational theory and effective one-component model have been used to calculate the Hugoniot equation of state (EOS) of fluid He, D2, and He+D2 mixtures with different He:D2 compositions under high pressu...The fluid variational theory and effective one-component model have been used to calculate the Hugoniot equation of state (EOS) of fluid He, D2, and He+D2 mixtures with different He:D2 compositions under high pressures and temperatures. An examination of the confidence of above computation is performed by comparing experiment and calculation, in which the similar calculation procedure used for He+D2 is adopted, of He and D2 each, since no experimental data are available to conduct this kind of comparison. Good agreement in both comparisons is found. This fact may be looked as if an indirect positive verification of calculation procedure used here at least in the pressure and temperature domain covered by the experimental data of He and D2 used for comparison, numerically nearly up to 35 GPa and 105K.展开更多
基金The authors thank the funds supported by the China National Nuclear Corporation under Grants Nos.WUQNYC2101 and WUHTLM2101-04National Natural Science Foundation of China(42074132,42274154).
文摘3D eikonal equation is a partial differential equation for the calculation of first-arrival traveltimes and has been widely applied in many scopes such as ray tracing,source localization,reflection migration,seismic monitoring and tomographic imaging.In recent years,many advanced methods have been developed to solve the 3D eikonal equation in heterogeneous media.However,there are still challenges for the stable and accurate calculation of first-arrival traveltimes in 3D strongly inhomogeneous media.In this paper,we propose an adaptive finite-difference(AFD)method to numerically solve the 3D eikonal equation.The novel method makes full use of the advantages of different local operators characterizing different seismic wave types to calculate factors and traveltimes,and then the most accurate factor and traveltime are adaptively selected for the convergent updating based on the Fermat principle.Combined with global fast sweeping describing seismic waves propagating along eight directions in 3D media,our novel method can achieve the robust calculation of first-arrival traveltimes with high precision at grid points either near source point or far away from source point even in a velocity model with large and sharp contrasts.Several numerical examples show the good performance of the AFD method,which will be beneficial to many scientific applications.
基金supported by China Postdoctoral Science Foundation (2020TQ0053 and 2020M680456)the research funds of Qianshixinmiao[2022]B16,Qianjiaoji[2022]124 and Qiankehepingtairencai-YSZ[2022]022+1 种基金supported by the NSFC (11731014 and 11571254)supported by the NSFC (11971067,11631008,11771183)。
文摘Several new concepts of enhanced pullback attractors for nonautonomous dynamical systems are introduced here by uniformly enhancing the compactness and attraction of the usual pullback attractors over an infinite forward time-interval under strong and weak topologies.Then we provide some theoretical results for the existence,regularity and asymptotic stability of these enhanced pullback attractors under general theoretical frameworks which can be applied to a large class of PDEs.The existence of these enhanced attractors is harder to obtain than the backward case[33],since it is difficult to uniformly control the long-time pullback behavior of the systems over the forward time-interval.As applications of our theoretical results,we consider the famous 3D primitive equations modelling the large-scale ocean and atmosphere dynamics,and prove the existence,regularity and asymptotic stability of the enhanced pullback attractors in V×V and H^(2)×H^(2) for the time-dependent forces which satisfy some weak conditions.
基金Project supported by the National Natural Science Foundation of China(Nos.11672265,11202182,and 11621062)the Fundamental Research Funds for the Central Universities(Nos.2016QNA4026 and2016XZZX001-05)the Open Foundation of Zhejiang Provincial Top Key Discipline of Mechanical Engineering
文摘A theoretical model is developed for predicting both conduction and diffusion in thin-film ionic conductors or cables. With the linearized Poisson-Nernst-Planck(PNP)theory, the two-dimensional(2D) equations for thin ionic conductor films are obtained from the three-dimensional(3D) equations by power series expansions in the film thickness coordinate, retaining the lower-order equations. The thin-film equations for ionic conductors are combined with similar equations for one thin dielectric film to derive the 2D equations of thin sandwich films composed of a dielectric layer and two ionic conductor layers. A sandwich film in the literature, as an ionic cable, is analyzed as an example of the equations obtained in this paper. The numerical results show the effect of diffusion in addition to the conduction treated in the literature. The obtained theoretical model including both conduction and diffusion phenomena can be used to investigate the performance of ionic-conductor devices with any frequency.
基金funded by the National Natural Science Foundation of China(Grant No.NSFC51374147)the German Society for Petroleum and Coal Science and Technology(Grant No.DGMK680-4)
文摘As one of the most important ways to reduce the greenhouse gas emission,carbon dioxide(CO2)enhanced gas recovery(CO2-EGR) is attractive since the gas recovery can be enhanced simultaneously with CO2sequestration.Based on the existing equation of state(EOS) module of TOUGH2 MP,extEOS7C is developed to calculate the phase partition of H2O-CO2-CH4-NaCl mixtures accurately with consideration of dissolved NaCI and brine properties at high pressure and temperature conditions.Verifications show that it can be applied up to the pressure of 100 MPa and temperature of 150℃.The module was implemented in the linked simulator TOUGH2MP-FLAC3 D for the coupled hydro-mechanical simulations.A simplified three-dimensional(3D)1/4 model(2.2 km×1 km×1 km) which consists of the whole reservoir,caprock and baserock was generated based on the geological conditions of a gas field in the North German Basin.The simulation results show that,under an injection rate of 200,000 t/yr and production rate of 200,000 sm3/d,CO2breakthrough occurred in the case with the initial reservoir pressure of 5 MPa but did not occur in the case of 42 MPa.Under low pressure conditions,the pressure driven horizontal transport is the dominant process;while under high pressure conditions,the density driven vertical flow is dominant.Under the considered conditions,the CO2-EGR caused only small pressure changes.The largest pore pressure increase(2 MPa) and uplift(7 mm) occurred at the caprock bottom induced by only CO2injection.The caprock had still the primary stress state and its integrity was not affected.The formation water salinity and temperature variations of ±20℃ had small influences on the CO2-EGR process.In order to slow down the breakthrough,it is suggested that CO2-EGR should be carried out before the reservoir pressure drops below the critical pressure of CO2.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11072218 and 10672143)
文摘This paper obtains Lagrange equations of nonholonomic systems with fractional derivatives. First, the exchanging relationships between the isochronous variation and the fractional derivatives are derived. Secondly, based on these exchanging relationships, the Hamilton's principle is presented for non-conservative systems with fractional derivatives. Thirdly, Lagrange equations of the systems are obtained. Furthermore, the d'Alembert-Lagrange principle with fractional derivatives is presented, and the Lagrange equations of nonholonomic systems with fractional derivatives are studied. An example is designed to illustrate these results.
文摘In this paper,we proposal stream surface and stream layer.By using classical tensor calculus,we derive 3-D Navier-Stokes Equations(NSE)in the stream layer under semigeodesic coordinate system,Navier-Stokes equation on the stream surface and 2-D Navier-Stokes equations on a two dimensional manifold. After introducing stream function on the stream surface,a nonlinear initial-boundary value problem satisfies by stream function is obtained,existence and uniqueness of its solution are proven.Based this theory we proposal a new method called"dimension split method"to solve 3D NSE.
基金The project supported by the National Natural Science Foundation of China(40276008)the Grant of Key Laboratory of Marine Science and Numerical Modeling.SOA(0201(2003))
文摘To further study the nal solitons on the continental fission laws of initial intershelf/slope, we rederive and correct the 2D KdV equation of Djordjevic & Redekopp for exponentially stratified fluid (or ocean) and with twodimensional topography. Through a combination of theoretical study and numerical experiments, we show that solitons in the odd vertical modes can fission. However, because of the corrections, the fission conditions are different from those of Djordjevic & Redekopp. The even modes cannot fission unless the initial internal solitons propagate from shallow sea to deep sea. This conclusion is entirely opposite to that of Djordjevic & Redekopp.
基金supported by the Yunnan Provincial Applied Basic Research Program of China(No. KKSY201207019)
文摘A three-dimensional (3D) predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa- tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.
基金China Postdoctoral Science Foundation Under Grant No.20100480321National Basic Research Program of China Under Grant No. 2007CB714200
文摘In this paper, an explicit method is generalized from 1D and 2D models to a 3D model for numerical simulation of wave motion, and the corresponding recursion formulas are developed for 3D irregular grids. For uniform cubic grids, the approach used to establish stable formulas with 2M-order accuracy is discussed in detail, with M being a positive integer, and is illustrated by establishing second order (M=1) recursion formulas. The theoretical results presented in this paper are demonstrated through numerical testing.
基金supported by the National Natural Science Foundation of China (No. 10661002)the NaturalScience Foundation of Guangxi (No. 0832065)the Excellent Talents Fund of Guangxi (No. 0825)
文摘The 2D generalized stochastic Ginzburg-Landau equation with additive noise is considered. The compactness of the random dynamical system is established with a priori estimate method, showing that the random dynamical system possesses a random attractor in H^1 0.
文摘Two high-order splitting schemes based on the idea of the operators splitting method are given. The three-dimensional advection-diffusion equation was split into several one-dimensional equations that were solved by these two schemes, only three computational grid points were needed in each direction but the accuracy reaches the spatial fourth-order. The third scheme proposed is based on the classical ADI scheme and the accuracy of the advection term of it can reach the spatial fourth-order. Finally, two typical numerical experiments show that the solutions of these three schemes compare well with that given by the analytical solution when the Peclet number is not bigger than 5.
基金Project supported by the National Natural Science Foundation of China(No.11074170)the State Key Laboratory Foundation of Shanghai Jiao Tong University(No.MSVMS201105)
文摘This paper describes formulation and implementation of the fast multipole boundary element method (FMBEM) for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the FMBEM are described in details. They are moment calculation, moment to moment translation, moment to local translation, and local to local translation. A data structure for the quad-tree construction is proposed which can facilitate implementation. An analytical moment expression is derived, which is more accurate, stable, and efficient than direct numerical computation. Numerical examples are presented to demonstrate the accuracy and efficiency of the FMBEM, and radiation of a 2D vibration rail mode is simulated using the FMBEM.
基金Project supported by the National Natural Science Foundation of China(Nos.11672223,11402187,and 51178390)the China Postdoctoral Science Foundation(No.2014M560762)the Fundamental Research Funds for the Central Universities of China(No.xjj2015131)
文摘Within the framework of continuum mechanics, the double power series ex- pansion technique is proposed, and a series of reduced one-dimensional (1D) equations for a piezoelectric semiconductor beam are obtained. These derived equations are universal, in which extension, flexure, and shear deformations are all included, and can be degen- erated to a number of special cases, e.g., extensional motion, coupled extensional and flexural motion with shear deformations, and elementary flexural motion without shear deformations. As a typical application, the extensional motion of a ZnO beam is analyzed sequentially. It is revealed that semi-conduction has a great effect on the performance of the piezoelectric semiconductor beam, including static deformations and dynamic be- haviors. A larger initial carrier density will evidently lead to a lower resonant frequency and a smaller displacement response, which is a little similar to the dissipative effect. Both the derived approximate equations and the corresponding qualitative analysis are general and widely applicable, which can clearly interpret the inner physical mechanism of the semiconductor in the piezoelectrics and provide theoretical guidance for further experimental design.
文摘A new method for solving the 1D Poisson equation is presented using the finite difference method. This method is based on the exact formulation of the inverse of the tridiagonal matrix associated with the Laplacian. This is the first time that the inverse of this remarkable matrix is determined directly and exactly. Thus, solving 1D Poisson equation becomes very accurate and extremely fast. This method is a very important tool for physics and engineering where the Poisson equation appears very often in the description of certain phenomena.
文摘In this paper we propose a numerical approach to solve the relativistic Dirac equation suitable for computational calculations of one-electron systems. A variational procedure is carried out similar to the well-known Hylleraas computational method. An application of the method to hydrogen isoelectronic atoms is presented, showing its consistency and high accuracy, relative to the exact analytical eigenvalues.
文摘We study the D-dimensional Schrodinger equation for an energy-dependent Hamiltonian that linearlydepends on energy and quadraticJy on the relative distance.Next,via the Nikiforov-Uvarov (NU) method,we calculatethe corresponding eigenfunctions and eigenvalues.
文摘The Rayleigh-Ritz and the inverse iteration methods are used in order to compute the eigenvalues of 3D Fredholm-Stieltjes integral equations, i.e. 3D Fredholm equations with respect to suitable Stieltjes-type measures. Some applications are shown, relevant to the problem of computing the eigenvalues of a body charged by a finite number of masses concentrated on points, curves or surfaces lying in.
文摘DC Resistivity Tomography is a non-linear inversion problem. So far there are mainly two kinds of inversion methods, based on the finite-element method and alpha centers method. In this paper, the disadvantages of these two kinds of methods were analysed,and a new method of forward modeling and inversion (Tomography) based on boundary integral equations was proposed. This scheme successfuly overcomes the difficulties of the two formarly methods. It isn’t necessary to use the linearization approximation and calculate the Jacobi matrix. Numerical modeling results given in this paper showed that the computation speed of our method is fast, and there is not any special requirement for initial model, and satisfying results of tomography can be obtained in the case of great contrast of conductivity. So it has wide applications.
文摘A physically-based numerical three-dimensional earthen dam piping failure model is developed for homogeneous and zoned soil dams.This model is an erosion model,coupled with force/moment equilibrium analyses.Orifice flow and two-dimensional(2D)shallow water equations(SWE)are solved to simulate dam break flows at different breaching stages.Erosion rates of different soils with different construction compaction efforts are calculated using corresponding erosion formulae.The dam's real shape,soil properties,and surrounding area are programmed.Large outer 2D-SWE grids are used to control upstream and downstream hydraulic conditions and control the boundary conditions of orifice flow,and inner 2D-SWE flow is used to scour soil and perform force/moment equilibrium analyses.This model is validated using the European Commission IMPACT(Investigation of Extreme Flood Processes and Uncertainty)Test#5 in Norway,Teton Dam failure in Idaho,USA,and Quail Creek Dike failure in Utah,USA.All calculated peak outflows are within 10%errors of observed values.Simulation results show that,for a V-shaped dam like Teton Dam,a piping breach location at the abutment tends to result in a smaller peak breach outflow than the piping breach location at the dam's center;and if Teton Dam had broken from its center for internal erosion,a peak outflow of 117851 m'/s,which is 81%larger than the peak outflow of 65120 m3/s released from its right abutment,would have been released from Teton Dam.A lower piping inlet elevation tends to cause a faster/earlier piping breach than a higher piping inlet elevation.
文摘The fluid variational theory and effective one-component model have been used to calculate the Hugoniot equation of state (EOS) of fluid He, D2, and He+D2 mixtures with different He:D2 compositions under high pressures and temperatures. An examination of the confidence of above computation is performed by comparing experiment and calculation, in which the similar calculation procedure used for He+D2 is adopted, of He and D2 each, since no experimental data are available to conduct this kind of comparison. Good agreement in both comparisons is found. This fact may be looked as if an indirect positive verification of calculation procedure used here at least in the pressure and temperature domain covered by the experimental data of He and D2 used for comparison, numerically nearly up to 35 GPa and 105K.