The viscous fluid flow and heat transfer over a stretching(shrinking)and porous sheets of nonuniform thickness are investigated in this paper.The modeled problem is presented by utilizing the stretching(shrinking)and ...The viscous fluid flow and heat transfer over a stretching(shrinking)and porous sheets of nonuniform thickness are investigated in this paper.The modeled problem is presented by utilizing the stretching(shrinking)and porous velocities and variable thickness of the sheet and they are combined in a relation.Consequently,the new problem reproduces the different available forms of flow motion and heat transfer maintained over a stretching(shrinking)and porous sheet of variable thickness in one go.As a result,the governing equations are embedded in several parameters which can be transformed into classical cases of stretched(shrunk)flows over porous sheets.A set of general,unusual and new variables is formed to simplify the governing partial differential equations and boundary conditions.The final equations are compared with the classical models to get the validity of the current simulations and they are exactly matched with each other for different choices of parameters of the current problem when their values are properly adjusted and manipulated.Moreover,we have recovered the classical results for special and appropriate values of the parameters(δ_(1),δ_(2),δ_(3),c,and B).The individual and combined effects of all inputs from the boundary are seen on flow and heat transfer properties with the help of a numerical method and the results are compared with classical solutions in special cases.It is noteworthy that the problem describes and enhances the behavior of all field quantities in view of the governing parameters.Numerical result shows that the dual solutions can be found for different possible values of the shrinking parameter.A stability analysis is accomplished and apprehended in order to establish a criterion for the determinations of linearly stable and physically compatible solutions.The significant features and diversity of the modeled equations are scrutinized by recovering the previous problems of fluid flow and heat transfer from a uniformly heated sheet of variable(uniform)thickness with variable(uniform)stretching/shrinking and injection/suction velocities.展开更多
To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’...To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.展开更多
An efficient numerical model for wave refraction, diffraction and reflection is presented in this paper. In the model the modified time-dependent mild-slope equation is transformed into an evolution equation and an im...An efficient numerical model for wave refraction, diffraction and reflection is presented in this paper. In the model the modified time-dependent mild-slope equation is transformed into an evolution equation and an improved ADI method involving a relaxation factor is adopted to solve it. The method has the advantage of improving the numerical stability and convergence rate by properly determining the relaxation factor. The range of the relaxation factor making the differential scheme unconditionally stable is determined by stability analysis. Several verifications are performed to examine the accuracy of the present model. The numerical results coincide with the analytic solutions or experimental data very well and the computer time is reduced.展开更多
Scale effect of ISWs loads on Floating Production Storage and Offloading(FPSO) is studied in this paper. The application conditions of KdV, eKdV and MCC ISWs theories are used in the numerical method. The depthaverage...Scale effect of ISWs loads on Floating Production Storage and Offloading(FPSO) is studied in this paper. The application conditions of KdV, eKdV and MCC ISWs theories are used in the numerical method. The depthaveraged velocities induced by ISWs are used for the velocity-inlet boundary. Three scale ratio numerical models λ=1, 20 and 300 were selected, which the scale ratio is the size ratio of numerical models to the experimental model.The comparisons between the numerical and former experimental results are performed to verify the feasibility of numerical method. The comparisons between the numerical and simplified theoretical results are performed to discuss the applicability of the simplified theoretical model summarized from the load experiments. Firstly, the numerical results of λ=1 numerical model showed a good agreement with former experimental and simplified theoretical results. It is feasible to simulate the ISWs loads on FPSO by the numerical method. Secondly, the comparisons between the results of three scale ratio numerical models and experimental results indicated that the scale ratios have more significant influence on the experimental horizontal forces than the vertical forces. The scale effect of horizontal forces mainly results from the different viscosity effects associated with the model’s dimension.Finally, through the comparisons between the numerical and simplified theoretical results for three scale ratio models, the simplified theoretical model of the pressure difference and friction forces exerted by ISWs on FPSO is applied for large-scale or full-scale FPSO.展开更多
The numerical solution for a type of quasilinear wave equation is studied.The three-level difference scheme for quasi-linear waver equation with strong dissipative term is constructed and the convergence is proved.The...The numerical solution for a type of quasilinear wave equation is studied.The three-level difference scheme for quasi-linear waver equation with strong dissipative term is constructed and the convergence is proved.The error of the difference solution is estimated.The theoretical results are controlled on a numerical example.展开更多
The exothermic efficiency of microwave heating an electrolyte/water solution is remarkably high due to the dielectric heating by orientation polarization of water and resistance heating by the Joule process occurred s...The exothermic efficiency of microwave heating an electrolyte/water solution is remarkably high due to the dielectric heating by orientation polarization of water and resistance heating by the Joule process occurred simultaneously compared with pure water.A three-dimensional finite element numerical model of multi-feed microwave heating industrial liquids continuously flowing in a meter-scale circular tube is presented.The temperature field inside the applicator tube in the cavity is solved by COMSOL Multiphysics and professional programming to describe the momentum,energy and Maxwell's equations.The evaluations of the electromagnetic field,the temperature distribution and the velocity field are simulated for the fluids dynamically heated by singleand multi-feed microwave system,respectively.Both the pilot experimental investigations and numerical results of microwave with single-feed heating for fluids with different effective permittivity and flow rates show that the presented numerical modeling makes it possible to analyze dynamic process of multi-feed microwave heating the industrial liquid.The study aids in enhancing the understanding and optimizing of dynamic process in the use of multi-feed microwave heating industrial continuous flow for a variety of material properties and technical parameters.展开更多
In this paper, authors discuss the numerical methods of general discontinuous boundary value problems for elliptic complex equations of first order, They first give the well posedness of general discontinuous boundary...In this paper, authors discuss the numerical methods of general discontinuous boundary value problems for elliptic complex equations of first order, They first give the well posedness of general discontinuous boundary value problems, reduce the discontinuous boundary value problems to a variation problem, and then find the numerical solutions of above problem by the finite element method. Finally authors give some error-estimates of the foregoing numerical solutions.展开更多
This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solutio...This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solution of test equations u'(t) = a 11 u(t) + a12v(t) + b11 u(t - τ1) + b12v(t-τ2,v'(t) = a21 u(t) + a22 v(t) + b21 u(t -τ1,) + b22 v(t -τ2), t>0,with initial conditionsu(t)=u0(t),v(t) =v0(t), t≤0.where aij, bij∈C, τj >0, i,j = 1,2,, and u0(t), v0(t)are continuous and complex valued. Sufficient conditions for the asymptotic stability of test equation are derived. Furthermore, with respect to an appropriate definition of stability for the numerical method, it is proved that the linear θ-method is stable if and only if 1/2≤θ≤1 and the one-leg θ-method is stable if and only if θ= 1.展开更多
The numerical analysis of heat transfer of laminar nanofluid flow over a fiat stretching sheet is presented. Two sets of boundary conditions （BCs） axe analyzed, i.e., a constant （Case 1） and a linear streamwise va...The numerical analysis of heat transfer of laminar nanofluid flow over a fiat stretching sheet is presented. Two sets of boundary conditions （BCs） axe analyzed, i.e., a constant （Case 1） and a linear streamwise variation of nanopaxticle volume fraction and wall temperature （Case 2）. The governing equations and BCs axe reduced to a set of nonlinear ordinary differential equations （ODEs） and the corresponding BCs, respectively. The dependencies of solutions on Prandtl number Pr, Lewis number Le, Brownian motion number Nb, and thermophoresis number Nt are studied in detail. The results show that the reduced Nusselt number and the reduced Sherwood number increase for the BCs of Case 2 compared with Case 1. The increases of Nb, Nt, and Le numbers cause a decrease of the reduced Nusselt number, while the reduced Sherwood number increases with the increase of Nb and Le numbers. For low Prandtl numbers, an increase of Nt number can cause to decrease in the reduced Sherwood number, while it increases for high Prandtl numbers.展开更多
The use of a shaped liner driven by electromagnetic force is a new means of forming jets. To study the mechanism of jet formation driven by electromagnetic force, we considered the current skin effect and the characte...The use of a shaped liner driven by electromagnetic force is a new means of forming jets. To study the mechanism of jet formation driven by electromagnetic force, we considered the current skin effect and the characteristics of electromagnetic loading and established a coupling model of "ElectriceMagnetic eForce" and the theoretical model of jet formation under electromagnetic force. The jet formation and penetration of conical and trumpet liners have been calculated. Then, a numerical simulation of liner collapse under electromagnetic force, jet generation, and the stretching motion were performed using an ANSYS multiphysics processor. The calculated jet velocity, jet shape, and depth of penetration were consistent with the experimental results, with a relative error of less than 10%. In addition, we calculated the jet formation of different curvature trumpet liners driven by the same loading condition and obtained the influence rule of the curvature of the liner on jet formation. Results show that the theoretical model and the ANSYS multiphysics numerical method can effectively calculate the jet formation of liners driven by electromagnetic force, and in a certain range, the greater the curvature of the liner is, the greater the jet velocity is.展开更多
In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarant...In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined.展开更多
To make heat conduction equation embody the essence of physical phenomenon under study, dimensionless factors were introduced and the transient heat conduction equation and its boundary conditions were transformed to ...To make heat conduction equation embody the essence of physical phenomenon under study, dimensionless factors were introduced and the transient heat conduction equation and its boundary conditions were transformed to dimensionless forms. Then, a theoretical solution model of transient heat conduction problem in one-dimensional double-layer composite medium was built utilizing the natural eigenfunction expansion method. In order to verify the validity of the model, the results of the above theoretical solution were compared with those of finite element method. The results by the two methods are in a good agreement. The maximum errors by the two methods appear when τ（τ is nondimensional time） equals 0.1 near the boundaries of ζ =1 （ζ is nondimensional space coordinate） and ζ =4. As τ increases, the error decreases gradually, and when τ =5 the results of both solutions have almost no change with the variation of coordinate 4.展开更多
Different factors affecting the efficiency of the orifice energy dissipator were investigated based on a series of theoretical analyses and numerical simulations. The main factors investigated by dimension analysis we...Different factors affecting the efficiency of the orifice energy dissipator were investigated based on a series of theoretical analyses and numerical simulations. The main factors investigated by dimension analysis were identified, including the Reynolds number （Re）, the ratio of the orifice diameter to the inner diameter of the pipe （ did ）, and the ratio of distances between orifices to the inner diameter of the pipe （ LID ）. Then, numerical simulations were conducted with a k-ε two-equation turbulence model. The calculation results show the following： Hydraulic characteristics change dramatically as flow passes through the orifice, with abruptly increasing velocity and turbulent energy, and decreasing pressure. The turbulent energy appears to be low in the middle and high near the pipe wall. For the energy dissipation setup with only one orifice, when Re is smaller than 105, the orifice energy dissipation coefficient K increases rapidly with the increase of Re. When Re is larger than l05, K gradually stabilizes. As diD increases, K and the length of the recirculation region L1 show similar variation patterns, which inversely vary with diD. The function curves can be approximated as straight lines. For the energy dissipation model with two orifices, because of different incoming flows at different orifices, the energy dissipation coefficient of the second orifice （K2） is smaller than that of the first. If LID is less than 5, the K value of the LID model, depending on the variation of/（2, increases with the spacing between two orifices L, and an orifice cannot fulfill its energy dissipation function. If LID is greater than 5, K2 tends to be steady; thus, the K value of the LID model gradually stabilizes. Then, the flow fully develops, and L has almost no impact on the value of K.展开更多
An initial value problem was considered for a coupled differential system with multi-term Caputo type fractional derivatives. By means of nonlinear alternative of Leray-Schauder and Banach contraction principle,the ex...An initial value problem was considered for a coupled differential system with multi-term Caputo type fractional derivatives. By means of nonlinear alternative of Leray-Schauder and Banach contraction principle,the existence and uniqueness of solutions for the system were derived. Using a fractional predictorcorrector method, a numerical method was presented for the specified system. An example was given to illustrate the obtained results.展开更多
Practical resolution of consolidation problems that we often face requires an extensive and solid knowledge of the different parameters highlighted by the Terzaghi one-dimensional consolidation theory. This theory, wi...Practical resolution of consolidation problems that we often face requires an extensive and solid knowledge of the different parameters highlighted by the Terzaghi one-dimensional consolidation theory. This theory, with its assumptions, leads to a partial differential equation of second order in space and first order in time of pore water pressure. Analytical and numerical resolutions of this equation allow determining the water pressure variation before and after the application of a charge. Numerical modeling has enabled the simulation of the whole results obtained by the two methods of resolution (pressure, degree of consolidation, time factor, among others) to have a physical analysis and a lawful observation that lead to a suitable understanding of the phenomenon of Terzaghi one-dimensional consolidation.展开更多
A new algorithm is presented for solving Troesch’s problem. The numerical scheme based on the sinc-collocation technique is deduced. The equation is reduced to systems of nonlinear algebraic equations. Some numerical...A new algorithm is presented for solving Troesch’s problem. The numerical scheme based on the sinc-collocation technique is deduced. The equation is reduced to systems of nonlinear algebraic equations. Some numerical experiments are made. Compared with the modified homotopy perturbation technique (MHP), the variational iteration method and the Adomian decomposition method. It is shown that the sinc-collocation method yields better results.展开更多
The main goal of this work is to develop an effective technique for solving nonlinear systems of Volterra integral equations. The main tools are the cardinal spline functions on small compact supports. We solve a syst...The main goal of this work is to develop an effective technique for solving nonlinear systems of Volterra integral equations. The main tools are the cardinal spline functions on small compact supports. We solve a system of algebra equations to approximate the solution of the system of integral equations. Since the matrix for the algebraic system is nearly triangular, It is relatively painless to solve for the unknowns and an approximation of the original solution with high precision is accomplished. In order to enhance the accuracy, several cardinal splines are employed in the paper. Our schemes were compared with other techniques proposed in recent papers and the advantage of our method was exhibited with several numerical examples.展开更多
In this paper, the Adomian decomposition method is developed for the numerical solutions of a class of nonlinear evolution equations with nonlinear term of any order, utt＋auxx ＋ bu ＋ cu^p＋ du^2p-1=0, which contain...In this paper, the Adomian decomposition method is developed for the numerical solutions of a class of nonlinear evolution equations with nonlinear term of any order, utt＋auxx ＋ bu ＋ cu^p＋ du^2p-1=0, which contains some important famous equations. When setting the initial conditions in different forms, some new generalized numerical solutions： numerical hyperbolic solutions, numerical doubly periodic solutions are obtained. The numerical solutions are compared with exact solutions. The scheme is tested by choosing different values of p, positive and negative, integer and fraction, to illustrate the efficiency of the ADM method and the generalization of the solutions.展开更多
An exact analytic solution for wave diffraction by wedge or corner with arbitrary angle (rπ) and reflection coefficients (R0 and Rr) is presented in this paper. It is expressed in two forms-series and integral repres...An exact analytic solution for wave diffraction by wedge or corner with arbitrary angle (rπ) and reflection coefficients (R0 and Rr) is presented in this paper. It is expressed in two forms-series and integral representations, corresponding recurrence relation and asymptotic expressions are also derived. The solution is simplified for some special cases of rπ. For Rr= R0,r= 1/N and Rr≠R0,r = 1/2N, the solution can be reduced to linear superpositions of incident and partially reflected waves, hence a nonlinear solution of forth order for this problem can be obtained by using the author's theory of nonlinear interaction among gravity surface waves. The given solution is related to inhomogeneous Robin boundary conditions, which include the Neumann boundary conditions usually accepted in wave diffraction theory.展开更多
文摘The viscous fluid flow and heat transfer over a stretching(shrinking)and porous sheets of nonuniform thickness are investigated in this paper.The modeled problem is presented by utilizing the stretching(shrinking)and porous velocities and variable thickness of the sheet and they are combined in a relation.Consequently,the new problem reproduces the different available forms of flow motion and heat transfer maintained over a stretching(shrinking)and porous sheet of variable thickness in one go.As a result,the governing equations are embedded in several parameters which can be transformed into classical cases of stretched(shrunk)flows over porous sheets.A set of general,unusual and new variables is formed to simplify the governing partial differential equations and boundary conditions.The final equations are compared with the classical models to get the validity of the current simulations and they are exactly matched with each other for different choices of parameters of the current problem when their values are properly adjusted and manipulated.Moreover,we have recovered the classical results for special and appropriate values of the parameters(δ_(1),δ_(2),δ_(3),c,and B).The individual and combined effects of all inputs from the boundary are seen on flow and heat transfer properties with the help of a numerical method and the results are compared with classical solutions in special cases.It is noteworthy that the problem describes and enhances the behavior of all field quantities in view of the governing parameters.Numerical result shows that the dual solutions can be found for different possible values of the shrinking parameter.A stability analysis is accomplished and apprehended in order to establish a criterion for the determinations of linearly stable and physically compatible solutions.The significant features and diversity of the modeled equations are scrutinized by recovering the previous problems of fluid flow and heat transfer from a uniformly heated sheet of variable(uniform)thickness with variable(uniform)stretching/shrinking and injection/suction velocities.
文摘To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.
文摘An efficient numerical model for wave refraction, diffraction and reflection is presented in this paper. In the model the modified time-dependent mild-slope equation is transformed into an evolution equation and an improved ADI method involving a relaxation factor is adopted to solve it. The method has the advantage of improving the numerical stability and convergence rate by properly determining the relaxation factor. The range of the relaxation factor making the differential scheme unconditionally stable is determined by stability analysis. Several verifications are performed to examine the accuracy of the present model. The numerical results coincide with the analytic solutions or experimental data very well and the computer time is reduced.
基金financially supported by the National Natural Science Foundation of China(Grant No.11372184)the National Basic Research Program of China(973 Program,Grant Nos.2015CB251203-3 and 2013CB036103)
文摘Scale effect of ISWs loads on Floating Production Storage and Offloading(FPSO) is studied in this paper. The application conditions of KdV, eKdV and MCC ISWs theories are used in the numerical method. The depthaveraged velocities induced by ISWs are used for the velocity-inlet boundary. Three scale ratio numerical models λ=1, 20 and 300 were selected, which the scale ratio is the size ratio of numerical models to the experimental model.The comparisons between the numerical and former experimental results are performed to verify the feasibility of numerical method. The comparisons between the numerical and simplified theoretical results are performed to discuss the applicability of the simplified theoretical model summarized from the load experiments. Firstly, the numerical results of λ=1 numerical model showed a good agreement with former experimental and simplified theoretical results. It is feasible to simulate the ISWs loads on FPSO by the numerical method. Secondly, the comparisons between the results of three scale ratio numerical models and experimental results indicated that the scale ratios have more significant influence on the experimental horizontal forces than the vertical forces. The scale effect of horizontal forces mainly results from the different viscosity effects associated with the model’s dimension.Finally, through the comparisons between the numerical and simplified theoretical results for three scale ratio models, the simplified theoretical model of the pressure difference and friction forces exerted by ISWs on FPSO is applied for large-scale or full-scale FPSO.
基金Supported by the National Natural Science Foundation of China (No.50244012) the National Science Foundtion of Shaanxi Education Department (No.02JC37)
文摘The numerical solution for a type of quasilinear wave equation is studied.The three-level difference scheme for quasi-linear waver equation with strong dissipative term is constructed and the convergence is proved.The error of the difference solution is estimated.The theoretical results are controlled on a numerical example.
基金Project(KKSY201503006)supported by Scientific Research Foundation of Kunming University of Science and Technology,ChinaProject(2014FD009)supported by the Applied Basic Research Foundation(Youth Program)of ChinaProject(51090385)supported by the National Natural Science Foundation of China
文摘The exothermic efficiency of microwave heating an electrolyte/water solution is remarkably high due to the dielectric heating by orientation polarization of water and resistance heating by the Joule process occurred simultaneously compared with pure water.A three-dimensional finite element numerical model of multi-feed microwave heating industrial liquids continuously flowing in a meter-scale circular tube is presented.The temperature field inside the applicator tube in the cavity is solved by COMSOL Multiphysics and professional programming to describe the momentum,energy and Maxwell's equations.The evaluations of the electromagnetic field,the temperature distribution and the velocity field are simulated for the fluids dynamically heated by singleand multi-feed microwave system,respectively.Both the pilot experimental investigations and numerical results of microwave with single-feed heating for fluids with different effective permittivity and flow rates show that the presented numerical modeling makes it possible to analyze dynamic process of multi-feed microwave heating the industrial liquid.The study aids in enhancing the understanding and optimizing of dynamic process in the use of multi-feed microwave heating industrial continuous flow for a variety of material properties and technical parameters.
文摘In this paper, authors discuss the numerical methods of general discontinuous boundary value problems for elliptic complex equations of first order, They first give the well posedness of general discontinuous boundary value problems, reduce the discontinuous boundary value problems to a variation problem, and then find the numerical solutions of above problem by the finite element method. Finally authors give some error-estimates of the foregoing numerical solutions.
文摘This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solution of test equations u'(t) = a 11 u(t) + a12v(t) + b11 u(t - τ1) + b12v(t-τ2,v'(t) = a21 u(t) + a22 v(t) + b21 u(t -τ1,) + b22 v(t -τ2), t>0,with initial conditionsu(t)=u0(t),v(t) =v0(t), t≤0.where aij, bij∈C, τj >0, i,j = 1,2,, and u0(t), v0(t)are continuous and complex valued. Sufficient conditions for the asymptotic stability of test equation are derived. Furthermore, with respect to an appropriate definition of stability for the numerical method, it is proved that the linear θ-method is stable if and only if 1/2≤θ≤1 and the one-leg θ-method is stable if and only if θ= 1.
文摘The numerical analysis of heat transfer of laminar nanofluid flow over a fiat stretching sheet is presented. Two sets of boundary conditions （BCs） axe analyzed, i.e., a constant （Case 1） and a linear streamwise variation of nanopaxticle volume fraction and wall temperature （Case 2）. The governing equations and BCs axe reduced to a set of nonlinear ordinary differential equations （ODEs） and the corresponding BCs, respectively. The dependencies of solutions on Prandtl number Pr, Lewis number Le, Brownian motion number Nb, and thermophoresis number Nt are studied in detail. The results show that the reduced Nusselt number and the reduced Sherwood number increase for the BCs of Case 2 compared with Case 1. The increases of Nb, Nt, and Le numbers cause a decrease of the reduced Nusselt number, while the reduced Sherwood number increases with the increase of Nb and Le numbers. For low Prandtl numbers, an increase of Nt number can cause to decrease in the reduced Sherwood number, while it increases for high Prandtl numbers.
基金supported by the Natural Science Funds for Distinguished Young Scholar (Grant No. 11602110)Jiangsu Province Graduate Research and Practice Innovation Program (No.KY CX180471)。
文摘The use of a shaped liner driven by electromagnetic force is a new means of forming jets. To study the mechanism of jet formation driven by electromagnetic force, we considered the current skin effect and the characteristics of electromagnetic loading and established a coupling model of "ElectriceMagnetic eForce" and the theoretical model of jet formation under electromagnetic force. The jet formation and penetration of conical and trumpet liners have been calculated. Then, a numerical simulation of liner collapse under electromagnetic force, jet generation, and the stretching motion were performed using an ANSYS multiphysics processor. The calculated jet velocity, jet shape, and depth of penetration were consistent with the experimental results, with a relative error of less than 10%. In addition, we calculated the jet formation of different curvature trumpet liners driven by the same loading condition and obtained the influence rule of the curvature of the liner on jet formation. Results show that the theoretical model and the ANSYS multiphysics numerical method can effectively calculate the jet formation of liners driven by electromagnetic force, and in a certain range, the greater the curvature of the liner is, the greater the jet velocity is.
基金Supported by Russian Fund of Fund amental Investigations(Pr.990101064)and Russian Minister of Educatin
文摘In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined.
基金Projects(50576007,50876016) supported by the National Natural Science Foundation of ChinaProjects(20062180) supported by the National Natural Science Foundation of Liaoning Province,China
文摘To make heat conduction equation embody the essence of physical phenomenon under study, dimensionless factors were introduced and the transient heat conduction equation and its boundary conditions were transformed to dimensionless forms. Then, a theoretical solution model of transient heat conduction problem in one-dimensional double-layer composite medium was built utilizing the natural eigenfunction expansion method. In order to verify the validity of the model, the results of the above theoretical solution were compared with those of finite element method. The results by the two methods are in a good agreement. The maximum errors by the two methods appear when τ（τ is nondimensional time） equals 0.1 near the boundaries of ζ =1 （ζ is nondimensional space coordinate） and ζ =4. As τ increases, the error decreases gradually, and when τ =5 the results of both solutions have almost no change with the variation of coordinate 4.
文摘Different factors affecting the efficiency of the orifice energy dissipator were investigated based on a series of theoretical analyses and numerical simulations. The main factors investigated by dimension analysis were identified, including the Reynolds number （Re）, the ratio of the orifice diameter to the inner diameter of the pipe （ did ）, and the ratio of distances between orifices to the inner diameter of the pipe （ LID ）. Then, numerical simulations were conducted with a k-ε two-equation turbulence model. The calculation results show the following： Hydraulic characteristics change dramatically as flow passes through the orifice, with abruptly increasing velocity and turbulent energy, and decreasing pressure. The turbulent energy appears to be low in the middle and high near the pipe wall. For the energy dissipation setup with only one orifice, when Re is smaller than 105, the orifice energy dissipation coefficient K increases rapidly with the increase of Re. When Re is larger than l05, K gradually stabilizes. As diD increases, K and the length of the recirculation region L1 show similar variation patterns, which inversely vary with diD. The function curves can be approximated as straight lines. For the energy dissipation model with two orifices, because of different incoming flows at different orifices, the energy dissipation coefficient of the second orifice （K2） is smaller than that of the first. If LID is less than 5, the K value of the LID model, depending on the variation of/（2, increases with the spacing between two orifices L, and an orifice cannot fulfill its energy dissipation function. If LID is greater than 5, K2 tends to be steady; thus, the K value of the LID model gradually stabilizes. Then, the flow fully develops, and L has almost no impact on the value of K.
基金National Natural Science Foundation of China(No.11371087)
文摘An initial value problem was considered for a coupled differential system with multi-term Caputo type fractional derivatives. By means of nonlinear alternative of Leray-Schauder and Banach contraction principle,the existence and uniqueness of solutions for the system were derived. Using a fractional predictorcorrector method, a numerical method was presented for the specified system. An example was given to illustrate the obtained results.
文摘Practical resolution of consolidation problems that we often face requires an extensive and solid knowledge of the different parameters highlighted by the Terzaghi one-dimensional consolidation theory. This theory, with its assumptions, leads to a partial differential equation of second order in space and first order in time of pore water pressure. Analytical and numerical resolutions of this equation allow determining the water pressure variation before and after the application of a charge. Numerical modeling has enabled the simulation of the whole results obtained by the two methods of resolution (pressure, degree of consolidation, time factor, among others) to have a physical analysis and a lawful observation that lead to a suitable understanding of the phenomenon of Terzaghi one-dimensional consolidation.
文摘A new algorithm is presented for solving Troesch’s problem. The numerical scheme based on the sinc-collocation technique is deduced. The equation is reduced to systems of nonlinear algebraic equations. Some numerical experiments are made. Compared with the modified homotopy perturbation technique (MHP), the variational iteration method and the Adomian decomposition method. It is shown that the sinc-collocation method yields better results.
文摘The main goal of this work is to develop an effective technique for solving nonlinear systems of Volterra integral equations. The main tools are the cardinal spline functions on small compact supports. We solve a system of algebra equations to approximate the solution of the system of integral equations. Since the matrix for the algebraic system is nearly triangular, It is relatively painless to solve for the unknowns and an approximation of the original solution with high precision is accomplished. In order to enhance the accuracy, several cardinal splines are employed in the paper. Our schemes were compared with other techniques proposed in recent papers and the advantage of our method was exhibited with several numerical examples.
基金supported by National Natural Science Foundation of China under Grant No.10735030Natural Science Foundation of Zhejiang Province of China under Grant No.Y604056Doctoral Science Foundation of Ningbo City under Grant No.2005A61030
文摘In this paper, the Adomian decomposition method is developed for the numerical solutions of a class of nonlinear evolution equations with nonlinear term of any order, utt＋auxx ＋ bu ＋ cu^p＋ du^2p-1=0, which contains some important famous equations. When setting the initial conditions in different forms, some new generalized numerical solutions： numerical hyperbolic solutions, numerical doubly periodic solutions are obtained. The numerical solutions are compared with exact solutions. The scheme is tested by choosing different values of p, positive and negative, integer and fraction, to illustrate the efficiency of the ADM method and the generalization of the solutions.
文摘An exact analytic solution for wave diffraction by wedge or corner with arbitrary angle (rπ) and reflection coefficients (R0 and Rr) is presented in this paper. It is expressed in two forms-series and integral representations, corresponding recurrence relation and asymptotic expressions are also derived. The solution is simplified for some special cases of rπ. For Rr= R0,r= 1/N and Rr≠R0,r = 1/2N, the solution can be reduced to linear superpositions of incident and partially reflected waves, hence a nonlinear solution of forth order for this problem can be obtained by using the author's theory of nonlinear interaction among gravity surface waves. The given solution is related to inhomogeneous Robin boundary conditions, which include the Neumann boundary conditions usually accepted in wave diffraction theory.
