A least-squares finite-element method (LSFEM) for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercriti...A least-squares finite-element method (LSFEM) for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercritical flows, and flows with smooth and sharp gradient changes. Advantages of the model include: (1) sources terms, such as the bottom slope, surface stresses and bed frictions, can be treated easily without any special treatment; (2) upwind scheme is no needed; (3) a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi (LBB) condition; and (4) the resulting system of equations is symmetric and positive-definite (SPD) which can be solved efficiently with the preconditioned conjugate gradient method. The model is verified with flow over a bump, tide induced flow, and dam-break. Computed results are compared with analytic solutions or other numerical results, and show the model is conservative and accurate. The model is then used to simulate flow past a circular cylinder. Important flow charac-teristics, such as variation of water surface around the cylinder and vortex shedding behind the cylinder are investigated. Computed results compare well with experiment data and other numerical results.展开更多
The effect of axial shallow groove on the nonlinear dynamic response and buckling of laminated cylindrical shells subjected to radial compression loading was investigated. Based on the first-order shear deformation th...The effect of axial shallow groove on the nonlinear dynamic response and buckling of laminated cylindrical shells subjected to radial compression loading was investigated. Based on the first-order shear deformation theory (FSDT), the nonlinear dynamic equations involving the transverse shear deformation and initial geometric imperfections were derived with the Hamilton philosophy. The axial shallow groove of the laminated composite cylindrical shell was treated as the initial geometric imperfections in the dynamic equations. A semi-analytical method of expanding displacements and loads along the circumferential direction and employing the finite difference method along the axial direction and in the time domain is used to solve the governing equations and obtain the dynamic response of the laminated shell. The B-R criterion was employed to determine the critical loads of dynamic buckling of the shell. The effects of the parameters of the shallow groove on the dynamic response and buckling were discussed in this paper and the results show that the axial shallow grooves greatly affect the dynamic response and buckling.展开更多
Shallow layer method(SLM)based on the definition of the geoid can determine the gravity field inside the shallow layer.In this study,the orthometric height of Mount Everest(HME)is calculated based on SLM,in which the ...Shallow layer method(SLM)based on the definition of the geoid can determine the gravity field inside the shallow layer.In this study,the orthometric height of Mount Everest(HME)is calculated based on SLM,in which the key is to construct the shallow layer model.The top and bottom boundaries of the shallow layer model are the natural surface of the Earth and the surface at a certain depth below the reference geoid,respectively.The model-combined strategies to determine the geoid undulation(N)based on SLM are applied to calculate the HME by two approaches:(1)direct calculation by combining N and geodetic height(h);(2)calculation by the segment summation approach(SSA)using the gravity field inside the shallow layer.On December 8,2020,the Chinese and Nepalese governments announced an authoritative value of 8848.86 m,which is referred to a geoid determined by the International Height Reference System(IHRS)(i.e.,the geopotential is 62636853.4 m^(2) s^(-2)).Here,our results(combined strategies(1)EGM2008 and CRUST1.0,(2)EGM2008 and CRUST2.0,(3)EIGEN-6 C4 and CRUST1.0,and(4)EIGEN-6 C4 and CRUST2.0)are referred to the geoid defined by WGS84(i.e.,the geopotential is 62636851.7 m^(2) s^(-2)).The differences between our results and the authoritative value(8848.86 m)are 0.448 m,-0.009 m,-0.295 m,and -0.741 m by the first approach,and 0.539 m,0.083 m,-0.214 m,and -0.647 m by the second approach.When the reference surface WGS84 geoid is converted to the IHRS geoid,the differences are 0.620 m,0.163 m,-0.123 m,and -0.569 m by the first approach,and0.711 m,0.225 m,-0.042 m,and -0.475 m by the second approach.展开更多
A particular porosity method named "slot method" is implemented in a depth-integrated shallow water flow model (DIVAST) to simulate wetting and drying processes. Discussed is the relationship between the shape fac...A particular porosity method named "slot method" is implemented in a depth-integrated shallow water flow model (DIVAST) to simulate wetting and drying processes. Discussed is the relationship between the shape factors of the "slot" and the preset depth used in "wetting-drying" algorithm. Two typical tests are conducted to examine the performance of the method with the effect of the shape factors of the "slot" being checked in detail in the first test. Numerical results demonstrate that: 1 ) no additional effort to improve the finite difference scheme is needed to implement "slot method" in DIVAST, and 2) "slot method" will simulate wetting and diying processes correctly if the shape factors of the "slot" being selected properly.展开更多
Based on the data of field measurement and drilling in the Tongling area, a series of numerical simulations are carried out by using the 'Surplus Space Method' (SSM), which is first put forward in this paper a...Based on the data of field measurement and drilling in the Tongling area, a series of numerical simulations are carried out by using the 'Surplus Space Method' (SSM), which is first put forward in this paper and applied to predict the shallow-seated magmatic bodies. The results of the numerical simulations show the existence and the 3-D shape of a conical magmatic structure at a depth of-1000 m beneath the center of the area: its top offsets southwards and bifurcates to several branches, while its lower part stretches northeastwards and contracts rapidly to a point at about -1000 m depth. This point is reckoned to be a 'sink' of magma system, transferring ore materials and heat energy from the deep magma chamber to the sub-surface apophyses. The preliminary application of the SSM proves that it may be developed as a new detection means for determining the existence of shallow-seated magmatic bodies and analyzing their three-dimensional features.展开更多
This present study develops a 2-D numerical scheme to simulate the velocity and depth on the actual terrain by using shallow water equations. The computational approach uses the HLL scheme as a basic building block, t...This present study develops a 2-D numerical scheme to simulate the velocity and depth on the actual terrain by using shallow water equations. The computational approach uses the HLL scheme as a basic building block, treats the bottom slope by lateralizing the momentum flux, then refines the scheme using the Strang splitting to deal with the frictional source term. Besides, a decoupled algorithm is also adopted to compute the aggradation and degradation of bed-level elevation by using the Manning-Strickler formula and Exner’s relationship. The main purpose is to set up the window interface of 2-D numerical model and increase the realization of engineers on these characteristics of hydraulic treatment and maintenance.展开更多
The mixed finite element(MFE) methods for a shallow water equation system consisting of water dynamics equations,silt transport equation,and the equation of bottom topography change were derived.A fully discrete MFE s...The mixed finite element(MFE) methods for a shallow water equation system consisting of water dynamics equations,silt transport equation,and the equation of bottom topography change were derived.A fully discrete MFE scheme for the discrete_time along characteristics is presented and error estimates are established.The existence and convergence of MFE solution of the discrete current velocity,elevation of the bottom topography,thickness of fluid column,and mass rate of sediment is demonstrated.展开更多
In this paper, we consider two extended model equations for shallow water waves. We use Adomian’s decomposition method (ADM) to solve them. It is proved that this method is a very good tool for shallow water wave equ...In this paper, we consider two extended model equations for shallow water waves. We use Adomian’s decomposition method (ADM) to solve them. It is proved that this method is a very good tool for shallow water wave equations and the obtained solutions are shown graphically.展开更多
An initial-boundary value problem for shallow equation system consisting of water dynamics equations,silt transport equation, the equation of bottom topography change,and of some boundary and initial conditions is stu...An initial-boundary value problem for shallow equation system consisting of water dynamics equations,silt transport equation, the equation of bottom topography change,and of some boundary and initial conditions is studied, the existence of its generalized solution and semidiscrete mixed finite element(MFE) solution was discussed, and the error estimates of the semidiscrete MFE solution was derived.The error estimates are optimal.展开更多
Semi-implicit algorithms are popularly used to deal with the gravitational term in numerical models. In this paper, we adopt the method of characteristics to compute the solutions for gravity waves on a sphere directl...Semi-implicit algorithms are popularly used to deal with the gravitational term in numerical models. In this paper, we adopt the method of characteristics to compute the solutions for gravity waves on a sphere directly using a semi-Lagrangian advection scheme instead of the semi-implicit method in a shallow water model, to avoid expensive matrix inversions. Adoption of the semi-Lagrangian scheme renders the numerical model always stable for any Courant number, and which saves CPU time. To illustrate the effciency of the characteristic constrained interpolation profile (CIP) method, some numerical results are shown for idealized test cases on a sphere in the Yin-Yang grid system.展开更多
In this paper, we consider two extended model equations for shallow water waves. We use He’s variational iteration method (VIM) to solve them. It is proved that this method is a very good tool for shallow water wave ...In this paper, we consider two extended model equations for shallow water waves. We use He’s variational iteration method (VIM) to solve them. It is proved that this method is a very good tool for shallow water wave equations and the obtained solutions are shown graphically.展开更多
In the investigation of debris flow, the detection of the source area of the post-disaster debris flow is an important basis for evaluating the distribution of the debris flow accumulation layer and the subsequent con...In the investigation of debris flow, the detection of the source area of the post-disaster debris flow is an important basis for evaluating the distribution of the debris flow accumulation layer and the subsequent control. In this paper, a shallow high-resolution TEM is used to detect the debris flow source area in Dashigou village, Yongji County, Jilin Province. The purpose of this investigation is to determine the depth range of debris flow damage. The detection results show that there is an obvious low resistance zone at about 10 m depth along the survey line, which is in good agreement with the drilling data and the high density electrical detection. It is proved that the depth is the maximum impact depth of the debris flow. The practical engineering proves that the method has high resolution in shallow layer detection, high efficiency and convenience in field acquisition. The maximum detection depth range of this method is 30--40 m, which meets the requirements of high efficiency and accurate detection for regional debris flow source area, and has high practical application value.展开更多
The two-dimensional nonlinear shallow water equations in the presence of Coriolis force and bottom topography are solved numerically using the fractional steps method. The fractional steps method consists of splitting...The two-dimensional nonlinear shallow water equations in the presence of Coriolis force and bottom topography are solved numerically using the fractional steps method. The fractional steps method consists of splitting the multi-dimensional matrix inversion problem into an equivalent one dimensional problem which is successively integrated in every direction along the characteristics using the Riemann invariant associated with the cubic spline interpolation. The height and the velocity field of the shallow water equations over irregular bottom are discretized on a fixed Eulerian grid and time-stepped using the fractional steps method. Effects of the Coriolis force and the bottom topography for particular initial flows on the velocity components and the free surface elevation have been studied and the results are plotted.展开更多
In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its app...In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the system of shallow water wave equations and modified Liouville equation which play an important role in mathematical physics.展开更多
Based on the results by Wang,in this paper, the iterative method is presented for the study of large deflection nonlinear problem of laminated composite shallow shells and plates. The rectangular laminated composite s...Based on the results by Wang,in this paper, the iterative method is presented for the study of large deflection nonlinear problem of laminated composite shallow shells and plates. The rectangular laminated composite shallow shells have been analyzed. The results have been compared with the small deflection linear analytical solution and finite element nonlinear solution. The results proved that the solution coincide with small deflection linear analytical solution in the condition of the low loads and finite element nonlinear solution in the condition of the high loads.展开更多
In this paper we consider the nonlinear stability of a thin elastic circular shallow spherical shell under the action of uniform normal pressure with a clamped edge. When the geometrical parameter k is large, the unif...In this paper we consider the nonlinear stability of a thin elastic circular shallow spherical shell under the action of uniform normal pressure with a clamped edge. When the geometrical parameter k is large, the uniformly valid asymptotic solutions are obtained by means of the singular perturbation method. In addition, we give the analytic formula for determining the centre deflection and the critical load, and the stability curve is also derived. This paper is a continuation of the author's previous paper[11]展开更多
Numerical solution of shallow-water equations (SWE) has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of s...Numerical solution of shallow-water equations (SWE) has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include: the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.展开更多
Using the modified method of multiple scales, the nonlinear stability of a truncated shallow spherical shell of variable thickness with a nondeformable rigid body at the center under compound loads is investigated. Wh...Using the modified method of multiple scales, the nonlinear stability of a truncated shallow spherical shell of variable thickness with a nondeformable rigid body at the center under compound loads is investigated. When the geometrical parameter k is larger, the uniformly valid asymptotic solutions of this problem are obtained and the remainder terms are estimated.展开更多
A finite element method for analysis of pollutant dispersion in shallow water is presented. The analysis is divided into two parts : ( 1 ) computation of the velocity flow field and water surface elevation, and (2...A finite element method for analysis of pollutant dispersion in shallow water is presented. The analysis is divided into two parts : ( 1 ) computation of the velocity flow field and water surface elevation, and (2) computation of the pollutant concentration field from the dispersion model. The method was combined with an adaptive meshing technique to increase the solution accuracy, as well as to reduce the computational time and computer memory. The finite element formulation and the computer programs were validated by several examples that have known solutions. In addition, the capability of the combined method was demonstrated by analyzing pollutant dispersion in Chao Phraya River near the gulf of Thailand.展开更多
A Newton multigrid method is developed for one-dimensional (1D) and two- dimensional (2D) steady-state shallow water equations (SWEs) with topography and dry areas. The nonlinear system arising from the well-bal...A Newton multigrid method is developed for one-dimensional (1D) and two- dimensional (2D) steady-state shallow water equations (SWEs) with topography and dry areas. The nonlinear system arising from the well-balanced finite volume discretization of the steady-state SWEs is solved by the Newton method as the outer iteration and a geometric multigrid method with the block symmetric Gauss-Seidel smoother as the inner iteration. The proposed Newton multigrid method makes use of the local residual to regularize the Jacobian matrix of the Newton iteration, and can handle the steady- state problem with wet/dry transition. Several numerical experiments are conducted to demonstrate the efficiency, robustness, and well-balanced property of the proposed method. The relation between the convergence behavior of the Newton multigrid method and the distribution of the eigenvalues of the iteration matrix is detailedly discussed.展开更多
基金the National Science Council ot Taiwan,China for funding this research(Project no.:NSC 94-2218-E-035-011)
文摘A least-squares finite-element method (LSFEM) for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercritical flows, and flows with smooth and sharp gradient changes. Advantages of the model include: (1) sources terms, such as the bottom slope, surface stresses and bed frictions, can be treated easily without any special treatment; (2) upwind scheme is no needed; (3) a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi (LBB) condition; and (4) the resulting system of equations is symmetric and positive-definite (SPD) which can be solved efficiently with the preconditioned conjugate gradient method. The model is verified with flow over a bump, tide induced flow, and dam-break. Computed results are compared with analytic solutions or other numerical results, and show the model is conservative and accurate. The model is then used to simulate flow past a circular cylinder. Important flow charac-teristics, such as variation of water surface around the cylinder and vortex shedding behind the cylinder are investigated. Computed results compare well with experiment data and other numerical results.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10202013)
文摘The effect of axial shallow groove on the nonlinear dynamic response and buckling of laminated cylindrical shells subjected to radial compression loading was investigated. Based on the first-order shear deformation theory (FSDT), the nonlinear dynamic equations involving the transverse shear deformation and initial geometric imperfections were derived with the Hamilton philosophy. The axial shallow groove of the laminated composite cylindrical shell was treated as the initial geometric imperfections in the dynamic equations. A semi-analytical method of expanding displacements and loads along the circumferential direction and employing the finite difference method along the axial direction and in the time domain is used to solve the governing equations and obtain the dynamic response of the laminated shell. The B-R criterion was employed to determine the critical loads of dynamic buckling of the shell. The effects of the parameters of the shallow groove on the dynamic response and buckling were discussed in this paper and the results show that the axial shallow grooves greatly affect the dynamic response and buckling.
基金supported in part by the National Natural Science Foundations of China under Grants Nos.41631072,42030105,41721003,41804012,and 41874023。
文摘Shallow layer method(SLM)based on the definition of the geoid can determine the gravity field inside the shallow layer.In this study,the orthometric height of Mount Everest(HME)is calculated based on SLM,in which the key is to construct the shallow layer model.The top and bottom boundaries of the shallow layer model are the natural surface of the Earth and the surface at a certain depth below the reference geoid,respectively.The model-combined strategies to determine the geoid undulation(N)based on SLM are applied to calculate the HME by two approaches:(1)direct calculation by combining N and geodetic height(h);(2)calculation by the segment summation approach(SSA)using the gravity field inside the shallow layer.On December 8,2020,the Chinese and Nepalese governments announced an authoritative value of 8848.86 m,which is referred to a geoid determined by the International Height Reference System(IHRS)(i.e.,the geopotential is 62636853.4 m^(2) s^(-2)).Here,our results(combined strategies(1)EGM2008 and CRUST1.0,(2)EGM2008 and CRUST2.0,(3)EIGEN-6 C4 and CRUST1.0,and(4)EIGEN-6 C4 and CRUST2.0)are referred to the geoid defined by WGS84(i.e.,the geopotential is 62636851.7 m^(2) s^(-2)).The differences between our results and the authoritative value(8848.86 m)are 0.448 m,-0.009 m,-0.295 m,and -0.741 m by the first approach,and 0.539 m,0.083 m,-0.214 m,and -0.647 m by the second approach.When the reference surface WGS84 geoid is converted to the IHRS geoid,the differences are 0.620 m,0.163 m,-0.123 m,and -0.569 m by the first approach,and0.711 m,0.225 m,-0.042 m,and -0.475 m by the second approach.
基金the National Natural Science Foundation of China (Grant No.10702050)the Natural Science Foundation of Tianjin (Grant No.07JCYBJC07500)the Support Plan of Science and Technology of Tianjin (Grant No.07ZCGYSH01700)
文摘A particular porosity method named "slot method" is implemented in a depth-integrated shallow water flow model (DIVAST) to simulate wetting and drying processes. Discussed is the relationship between the shape factors of the "slot" and the preset depth used in "wetting-drying" algorithm. Two typical tests are conducted to examine the performance of the method with the effect of the shape factors of the "slot" being checked in detail in the first test. Numerical results demonstrate that: 1 ) no additional effort to improve the finite difference scheme is needed to implement "slot method" in DIVAST, and 2) "slot method" will simulate wetting and diying processes correctly if the shape factors of the "slot" being selected properly.
基金This study was financially supported by the National Important Basic Research and Development Planning Program(No.1999043206)the National Natural Science Foundation of China(No.40234051)+1 种基金the Special Plan of Science and Technology of the Ministry of Land and Resources(20010103)the"Trans-century Training Program for Outstanding Talents”Fund sponsored by the.Ministry of Education.
文摘Based on the data of field measurement and drilling in the Tongling area, a series of numerical simulations are carried out by using the 'Surplus Space Method' (SSM), which is first put forward in this paper and applied to predict the shallow-seated magmatic bodies. The results of the numerical simulations show the existence and the 3-D shape of a conical magmatic structure at a depth of-1000 m beneath the center of the area: its top offsets southwards and bifurcates to several branches, while its lower part stretches northeastwards and contracts rapidly to a point at about -1000 m depth. This point is reckoned to be a 'sink' of magma system, transferring ore materials and heat energy from the deep magma chamber to the sub-surface apophyses. The preliminary application of the SSM proves that it may be developed as a new detection means for determining the existence of shallow-seated magmatic bodies and analyzing their three-dimensional features.
文摘This present study develops a 2-D numerical scheme to simulate the velocity and depth on the actual terrain by using shallow water equations. The computational approach uses the HLL scheme as a basic building block, treats the bottom slope by lateralizing the momentum flux, then refines the scheme using the Strang splitting to deal with the frictional source term. Besides, a decoupled algorithm is also adopted to compute the aggradation and degradation of bed-level elevation by using the Manning-Strickler formula and Exner’s relationship. The main purpose is to set up the window interface of 2-D numerical model and increase the realization of engineers on these characteristics of hydraulic treatment and maintenance.
文摘The mixed finite element(MFE) methods for a shallow water equation system consisting of water dynamics equations,silt transport equation,and the equation of bottom topography change were derived.A fully discrete MFE scheme for the discrete_time along characteristics is presented and error estimates are established.The existence and convergence of MFE solution of the discrete current velocity,elevation of the bottom topography,thickness of fluid column,and mass rate of sediment is demonstrated.
文摘In this paper, we consider two extended model equations for shallow water waves. We use Adomian’s decomposition method (ADM) to solve them. It is proved that this method is a very good tool for shallow water wave equations and the obtained solutions are shown graphically.
文摘An initial-boundary value problem for shallow equation system consisting of water dynamics equations,silt transport equation, the equation of bottom topography change,and of some boundary and initial conditions is studied, the existence of its generalized solution and semidiscrete mixed finite element(MFE) solution was discussed, and the error estimates of the semidiscrete MFE solution was derived.The error estimates are optimal.
基金supported by National Natural Science Foundation of China (NSFC) projects (Grant Nos. 40875065 and 40805045)the research projects 2008R001 at Chinese Academy of Meteorological Sciences (CAMS) and 2008 LASWZI05 at the State Key Laboratory of Severe Weather, CAMS
文摘Semi-implicit algorithms are popularly used to deal with the gravitational term in numerical models. In this paper, we adopt the method of characteristics to compute the solutions for gravity waves on a sphere directly using a semi-Lagrangian advection scheme instead of the semi-implicit method in a shallow water model, to avoid expensive matrix inversions. Adoption of the semi-Lagrangian scheme renders the numerical model always stable for any Courant number, and which saves CPU time. To illustrate the effciency of the characteristic constrained interpolation profile (CIP) method, some numerical results are shown for idealized test cases on a sphere in the Yin-Yang grid system.
文摘In this paper, we consider two extended model equations for shallow water waves. We use He’s variational iteration method (VIM) to solve them. It is proved that this method is a very good tool for shallow water wave equations and the obtained solutions are shown graphically.
文摘In the investigation of debris flow, the detection of the source area of the post-disaster debris flow is an important basis for evaluating the distribution of the debris flow accumulation layer and the subsequent control. In this paper, a shallow high-resolution TEM is used to detect the debris flow source area in Dashigou village, Yongji County, Jilin Province. The purpose of this investigation is to determine the depth range of debris flow damage. The detection results show that there is an obvious low resistance zone at about 10 m depth along the survey line, which is in good agreement with the drilling data and the high density electrical detection. It is proved that the depth is the maximum impact depth of the debris flow. The practical engineering proves that the method has high resolution in shallow layer detection, high efficiency and convenience in field acquisition. The maximum detection depth range of this method is 30--40 m, which meets the requirements of high efficiency and accurate detection for regional debris flow source area, and has high practical application value.
文摘The two-dimensional nonlinear shallow water equations in the presence of Coriolis force and bottom topography are solved numerically using the fractional steps method. The fractional steps method consists of splitting the multi-dimensional matrix inversion problem into an equivalent one dimensional problem which is successively integrated in every direction along the characteristics using the Riemann invariant associated with the cubic spline interpolation. The height and the velocity field of the shallow water equations over irregular bottom are discretized on a fixed Eulerian grid and time-stepped using the fractional steps method. Effects of the Coriolis force and the bottom topography for particular initial flows on the velocity components and the free surface elevation have been studied and the results are plotted.
文摘In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the system of shallow water wave equations and modified Liouville equation which play an important role in mathematical physics.
文摘Based on the results by Wang,in this paper, the iterative method is presented for the study of large deflection nonlinear problem of laminated composite shallow shells and plates. The rectangular laminated composite shallow shells have been analyzed. The results have been compared with the small deflection linear analytical solution and finite element nonlinear solution. The results proved that the solution coincide with small deflection linear analytical solution in the condition of the low loads and finite element nonlinear solution in the condition of the high loads.
文摘In this paper we consider the nonlinear stability of a thin elastic circular shallow spherical shell under the action of uniform normal pressure with a clamped edge. When the geometrical parameter k is large, the uniformly valid asymptotic solutions are obtained by means of the singular perturbation method. In addition, we give the analytic formula for determining the centre deflection and the critical load, and the stability curve is also derived. This paper is a continuation of the author's previous paper[11]
基金the National Science Council of Taiwan for funding this research (NSC 96-2221-E-019-061).
文摘Numerical solution of shallow-water equations (SWE) has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include: the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.
文摘Using the modified method of multiple scales, the nonlinear stability of a truncated shallow spherical shell of variable thickness with a nondeformable rigid body at the center under compound loads is investigated. When the geometrical parameter k is larger, the uniformly valid asymptotic solutions of this problem are obtained and the remainder terms are estimated.
文摘A finite element method for analysis of pollutant dispersion in shallow water is presented. The analysis is divided into two parts : ( 1 ) computation of the velocity flow field and water surface elevation, and (2) computation of the pollutant concentration field from the dispersion model. The method was combined with an adaptive meshing technique to increase the solution accuracy, as well as to reduce the computational time and computer memory. The finite element formulation and the computer programs were validated by several examples that have known solutions. In addition, the capability of the combined method was demonstrated by analyzing pollutant dispersion in Chao Phraya River near the gulf of Thailand.
基金Project supported by the National Natural Science Foundation of China(Nos.91330205and 11421101)the National Key Research and Development Program of China(No.2016YFB0200603)
文摘A Newton multigrid method is developed for one-dimensional (1D) and two- dimensional (2D) steady-state shallow water equations (SWEs) with topography and dry areas. The nonlinear system arising from the well-balanced finite volume discretization of the steady-state SWEs is solved by the Newton method as the outer iteration and a geometric multigrid method with the block symmetric Gauss-Seidel smoother as the inner iteration. The proposed Newton multigrid method makes use of the local residual to regularize the Jacobian matrix of the Newton iteration, and can handle the steady- state problem with wet/dry transition. Several numerical experiments are conducted to demonstrate the efficiency, robustness, and well-balanced property of the proposed method. The relation between the convergence behavior of the Newton multigrid method and the distribution of the eigenvalues of the iteration matrix is detailedly discussed.