A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first ...A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.展开更多
A new general optimal principle of designing explicit finite difference method was obtained. Several applied cases were put forward to explain the uses of the principle. The validity of the principal was tested by a n...A new general optimal principle of designing explicit finite difference method was obtained. Several applied cases were put forward to explain the uses of the principle. The validity of the principal was tested by a numeric example.展开更多
Numerical simulation of complex flow fields with multi-scale structures is one of the most important and challenging branches of computational fluid dynamics. From linear analysis and numerical experiments it has been...Numerical simulation of complex flow fields with multi-scale structures is one of the most important and challenging branches of computational fluid dynamics. From linear analysis and numerical experiments it has been discovered that the higher-order accurate method can give reliable and efficient computational results, as well as better resolution of the complex flow fields with multi-scale structures. Compact finite difference schemes, which feature higher-order accuracy and spectral-like resolution with smaller stencils and easier application of boundary conditions, has attracted more and more interest and attention.展开更多
The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF me...The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF method to some complex-valued nonlinear evolutionary equations such as the nonlinear SchrSdinger （NLS） equation and the complex Ginzburg-Landau （GL） equation. Detailed algorithm formulation and practical implementation of cIIF method are performed. The numerical results indicate that this method is very accurate and efficient.展开更多
This paper considers pricing European options under the well-known of SVJ model of Bates and related computational methods. According to the no-arbitrage principle, we first derive a partial differential equation that...This paper considers pricing European options under the well-known of SVJ model of Bates and related computational methods. According to the no-arbitrage principle, we first derive a partial differential equation that the value of any European contingent claim should satisfy, where the asset price obeys the SVJ model. This equation is numerically solved by using the implicit- explicit backward difference method and time semi-discretization. In order to explain the validity of our method, the stability of time semi-discretization scheme is also proved. Finally, we use a simulation example to illustrate the efficiency of the method.展开更多
A new algorithm based on the projection method with the implicit finite difference technique was established to calculate the velocity fields and pressure.The calculation region can be divided into different regions a...A new algorithm based on the projection method with the implicit finite difference technique was established to calculate the velocity fields and pressure.The calculation region can be divided into different regions according to Reynolds number.In the far-wall region,the thermal melt flow was calculated as Newtonian flow.In the near-wall region,the thermal melt flow was calculated as non-Newtonian flow.It was proved that the new algorithm based on the projection method with the implicit technique was correct through nonparametric statistics method and experiment.The simulation results show that the new algorithm based on the projection method with the implicit technique calculates more quickly than the solution algorithm-volume of fluid method using the explicit difference method.展开更多
针对COB-LED(Chip on Board-Light Emitting Diode)散热问题,文中基于二维热传导方程建立了一个可快速计算COB-LED散热器表面热分布的数学模型。为了便于模型求解,采用有限差分法求解该数学模型并选择交替方向隐格式作为其差分格式。根...针对COB-LED(Chip on Board-Light Emitting Diode)散热问题,文中基于二维热传导方程建立了一个可快速计算COB-LED散热器表面热分布的数学模型。为了便于模型求解,采用有限差分法求解该数学模型并选择交替方向隐格式作为其差分格式。根据模型中的边界条件和初始条件设计COB-LED常温点亮实验,并基于ANSYS有限元分析软件进行仿真分析。通过比较求解结果、仿真结果和实验结果验证该数学模型的合理性。结果表明,求解结果与实验结果中最高温度相对误差约23.57%,且两者的温度变化趋势一致。求解结果与仿真结果中最高温度相对误差约34.84%,且温度分布较为接近,证明了该数学模型的合理性与正确性。展开更多
Heat transfers due to MHD-conjugate free convection from the isothermal horizontal circular cylinder while viscosity is a function of temperature is investigated. The governing equations of the flow and connected boun...Heat transfers due to MHD-conjugate free convection from the isothermal horizontal circular cylinder while viscosity is a function of temperature is investigated. The governing equations of the flow and connected boundary conditions are made dimensionless using a set of non-dimensional parameters. The governing equations are solved numerically using the finite difference method. Numerical results are obtained for various values of viscosity variation parameter, Prandtl number, magnetic parameter, and conjugate conduction parameter for the velocity and the temperature within the boundary layer as well as the skin friction coefficients and heat transfer rate along the surface.展开更多
In order to eliminate Courant-Friedrich-Levy(CFL) condition restraint and improvecomputational efficiency,a new finite-difference time-domain(FDTD)method based on the alternating-direction implicit(ADI) technique is i...In order to eliminate Courant-Friedrich-Levy(CFL) condition restraint and improvecomputational efficiency,a new finite-difference time-domain(FDTD)method based on the alternating-direction implicit(ADI) technique is introduced recently.In this paper,a theoretical proof of the stabilityof the three-dimensional(3-D)ADI-FDTD method is presented.It is shown that the 3-D ADI-FDTDmethod is unconditionally stable and free from the CFL condition restraint.展开更多
Determining the venting time of a gas trunk pipeline segment provides an important basis for formulating an emergency plan in the advent of unexpected accidents.As the natural gas venting process corresponds to the tr...Determining the venting time of a gas trunk pipeline segment provides an important basis for formulating an emergency plan in the advent of unexpected accidents.As the natural gas venting process corresponds to the transient flow,it is necessary to establish a transient hydraulic-thermal simulation model in order to determine the venting time.In this paper,based on two kinds of venting scenarios in which there is only one venting point in the venting system of a gas trunk pipeline segment—namely,where the venting point is either at one of the two ends or at the junction of two gas trunk pipeline segments—transient hydraulic-thermal simulation models are established.The models consist of gas flow governing equations,the gas state equation,gas physical property equations,initial conditions,and appropriate boundary conditions.The implicit central difference method is used to discretize the gas flow partial differential equations,and the trust-region-dogleg algorithm is used to solve the equations corresponding to each time step,in order to dynamically simulate the whole venting process.The judgment condition for the end of the venting process is that the average pressure of gas trunk pipeline segment is less than 0.11 MPa(actual pressure).Comparing the simulation results of the proposed model with those of the OLGA software and real operational data,we find that the venting time error is less than 10%.On this basis,a venting valve opening control principle is proposed,which prevents the venting noise from exceeded the specified noise value(85 d B)in the venting design of domestic gas pipeline projects.The established calculation model for venting time(dynamic simulation model)for a gas trunk pipeline segment and the proposed opening control principle of venting valve provide reference for the optimal operation of gas pipeline venting systems.展开更多
A mathematical model comprising of nonlinear reaction, diffusion, and convection mechanisms seen in natural and anthropogenic processes is numerically investigated here. It is proposed that a higher order numerical sc...A mathematical model comprising of nonlinear reaction, diffusion, and convection mechanisms seen in natural and anthropogenic processes is numerically investigated here. It is proposed that a higher order numerical scheme of finite difference method be used in conjunction with an iterative approach in order to solve the nonlinear one dimensional convection-diffusion-reaction equation. To account for the wide variety of physical characteristics and boundary conditions, an iterative approach is presented that yields a reliable and precise solution every time. We examined the accuracy and operational efficiency of two distinct finite difference approaches. The efficiency of the system is determined by comparing the estimated results to the appropriate analytical solution by adhering to established norms. Coherence and convergence were analyzed for each approach. The simulation results demonstrate the efficacy and accuracy of these methods in solving nonlinear convection- diffusion-reaction equations. Convection-diffusion-reaction equation modeling is critical for employing the offered results in heat and mass transport processes.展开更多
In this paper, we consider the existence, uniqueness and convergence of weak and strongimplicit difference solution for the first boundary problem of quasilinear parabolic system: u_t=(-1)^(M+1)A(x,t,u,…,u_x^(M-1))u_...In this paper, we consider the existence, uniqueness and convergence of weak and strongimplicit difference solution for the first boundary problem of quasilinear parabolic system: u_t=(-1)^(M+1)A(x,t,u,…,u_x^(M-1))u_x^(2M)+f(x,t,u,…,u_x^(2M-1)), (x,t)∈Q_T={0<x<l, 0<t≤T}, (1) u_xk(0,t)=u_xk(l,t)=0,(k=0,1,…,M-1), 0<t≤T, (2) u(x,0) =ψ(x), 0≤x≤l, (3)where u, ψ and f are m-dimensional vector valued functions, A is an m×m positivelydefinite matrix and u_xk denotes ?~ku/?_xk. For this problem, the estimations of the differencesolution are obtained. As h→0, △t→0, the difference solution converges weakly in W_2^(2M,1) (QT)to the unique generalized solution u(x,t)∈W_2^(2M,1)(QT) of problems (1), (2), (3). Especially,a favorable restriction condition to the step lengths △t and h for explicit and weak implicitschemes is found.展开更多
文摘A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.
文摘A new general optimal principle of designing explicit finite difference method was obtained. Several applied cases were put forward to explain the uses of the principle. The validity of the principal was tested by a numeric example.
文摘Numerical simulation of complex flow fields with multi-scale structures is one of the most important and challenging branches of computational fluid dynamics. From linear analysis and numerical experiments it has been discovered that the higher-order accurate method can give reliable and efficient computational results, as well as better resolution of the complex flow fields with multi-scale structures. Compact finite difference schemes, which feature higher-order accuracy and spectral-like resolution with smaller stencils and easier application of boundary conditions, has attracted more and more interest and attention.
文摘The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF method to some complex-valued nonlinear evolutionary equations such as the nonlinear SchrSdinger （NLS） equation and the complex Ginzburg-Landau （GL） equation. Detailed algorithm formulation and practical implementation of cIIF method are performed. The numerical results indicate that this method is very accurate and efficient.
文摘This paper considers pricing European options under the well-known of SVJ model of Bates and related computational methods. According to the no-arbitrage principle, we first derive a partial differential equation that the value of any European contingent claim should satisfy, where the asset price obeys the SVJ model. This equation is numerically solved by using the implicit- explicit backward difference method and time semi-discretization. In order to explain the validity of our method, the stability of time semi-discretization scheme is also proved. Finally, we use a simulation example to illustrate the efficiency of the method.
基金Project (50975263) supported by the National Natural Science Foundation of ChinaProject (2010081015) supported by International Cooperation Project of Shanxi Province, China+1 种基金 Project (2010-78) supported by the Scholarship Council in Shanxi province, ChinaProject (2010420120005) supported by Doctoral Fund of Ministry of Education of China
文摘A new algorithm based on the projection method with the implicit finite difference technique was established to calculate the velocity fields and pressure.The calculation region can be divided into different regions according to Reynolds number.In the far-wall region,the thermal melt flow was calculated as Newtonian flow.In the near-wall region,the thermal melt flow was calculated as non-Newtonian flow.It was proved that the new algorithm based on the projection method with the implicit technique was correct through nonparametric statistics method and experiment.The simulation results show that the new algorithm based on the projection method with the implicit technique calculates more quickly than the solution algorithm-volume of fluid method using the explicit difference method.
文摘针对COB-LED(Chip on Board-Light Emitting Diode)散热问题,文中基于二维热传导方程建立了一个可快速计算COB-LED散热器表面热分布的数学模型。为了便于模型求解,采用有限差分法求解该数学模型并选择交替方向隐格式作为其差分格式。根据模型中的边界条件和初始条件设计COB-LED常温点亮实验,并基于ANSYS有限元分析软件进行仿真分析。通过比较求解结果、仿真结果和实验结果验证该数学模型的合理性。结果表明,求解结果与实验结果中最高温度相对误差约23.57%,且两者的温度变化趋势一致。求解结果与仿真结果中最高温度相对误差约34.84%,且温度分布较为接近,证明了该数学模型的合理性与正确性。
文摘Heat transfers due to MHD-conjugate free convection from the isothermal horizontal circular cylinder while viscosity is a function of temperature is investigated. The governing equations of the flow and connected boundary conditions are made dimensionless using a set of non-dimensional parameters. The governing equations are solved numerically using the finite difference method. Numerical results are obtained for various values of viscosity variation parameter, Prandtl number, magnetic parameter, and conjugate conduction parameter for the velocity and the temperature within the boundary layer as well as the skin friction coefficients and heat transfer rate along the surface.
基金Supported by the Specialized Research Fund for the Doctoral Program of Higher Education(No.20010614003)
文摘In order to eliminate Courant-Friedrich-Levy(CFL) condition restraint and improvecomputational efficiency,a new finite-difference time-domain(FDTD)method based on the alternating-direction implicit(ADI) technique is introduced recently.In this paper,a theoretical proof of the stabilityof the three-dimensional(3-D)ADI-FDTD method is presented.It is shown that the 3-D ADI-FDTDmethod is unconditionally stable and free from the CFL condition restraint.
基金supported by the National Natural Science Foundation of China(Grant No.52174064)
文摘Determining the venting time of a gas trunk pipeline segment provides an important basis for formulating an emergency plan in the advent of unexpected accidents.As the natural gas venting process corresponds to the transient flow,it is necessary to establish a transient hydraulic-thermal simulation model in order to determine the venting time.In this paper,based on two kinds of venting scenarios in which there is only one venting point in the venting system of a gas trunk pipeline segment—namely,where the venting point is either at one of the two ends or at the junction of two gas trunk pipeline segments—transient hydraulic-thermal simulation models are established.The models consist of gas flow governing equations,the gas state equation,gas physical property equations,initial conditions,and appropriate boundary conditions.The implicit central difference method is used to discretize the gas flow partial differential equations,and the trust-region-dogleg algorithm is used to solve the equations corresponding to each time step,in order to dynamically simulate the whole venting process.The judgment condition for the end of the venting process is that the average pressure of gas trunk pipeline segment is less than 0.11 MPa(actual pressure).Comparing the simulation results of the proposed model with those of the OLGA software and real operational data,we find that the venting time error is less than 10%.On this basis,a venting valve opening control principle is proposed,which prevents the venting noise from exceeded the specified noise value(85 d B)in the venting design of domestic gas pipeline projects.The established calculation model for venting time(dynamic simulation model)for a gas trunk pipeline segment and the proposed opening control principle of venting valve provide reference for the optimal operation of gas pipeline venting systems.
文摘A mathematical model comprising of nonlinear reaction, diffusion, and convection mechanisms seen in natural and anthropogenic processes is numerically investigated here. It is proposed that a higher order numerical scheme of finite difference method be used in conjunction with an iterative approach in order to solve the nonlinear one dimensional convection-diffusion-reaction equation. To account for the wide variety of physical characteristics and boundary conditions, an iterative approach is presented that yields a reliable and precise solution every time. We examined the accuracy and operational efficiency of two distinct finite difference approaches. The efficiency of the system is determined by comparing the estimated results to the appropriate analytical solution by adhering to established norms. Coherence and convergence were analyzed for each approach. The simulation results demonstrate the efficacy and accuracy of these methods in solving nonlinear convection- diffusion-reaction equations. Convection-diffusion-reaction equation modeling is critical for employing the offered results in heat and mass transport processes.
文摘In this paper, we consider the existence, uniqueness and convergence of weak and strongimplicit difference solution for the first boundary problem of quasilinear parabolic system: u_t=(-1)^(M+1)A(x,t,u,…,u_x^(M-1))u_x^(2M)+f(x,t,u,…,u_x^(2M-1)), (x,t)∈Q_T={0<x<l, 0<t≤T}, (1) u_xk(0,t)=u_xk(l,t)=0,(k=0,1,…,M-1), 0<t≤T, (2) u(x,0) =ψ(x), 0≤x≤l, (3)where u, ψ and f are m-dimensional vector valued functions, A is an m×m positivelydefinite matrix and u_xk denotes ?~ku/?_xk. For this problem, the estimations of the differencesolution are obtained. As h→0, △t→0, the difference solution converges weakly in W_2^(2M,1) (QT)to the unique generalized solution u(x,t)∈W_2^(2M,1)(QT) of problems (1), (2), (3). Especially,a favorable restriction condition to the step lengths △t and h for explicit and weak implicitschemes is found.
