Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditi...Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions. The electric potential is defined by an ellip- tic equation and it appears in the following three equations via the electric field intensity. The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation. A mixed finite volume element approximation, keeping physical conservation law, is used to get numerical values of the electric potential and the accuracy is improved one order. Two con- centrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences. This method can overcome numerical oscillation, dispersion and decreases computational complexity. Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened. An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations. This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.展开更多
In this paper, based on the improved complex variable moving least-square (ICVMLS) approximation, a new complex variable meshless method (CVMM) for two-dimensional (2D) transient heat conduction problems is pres...In this paper, based on the improved complex variable moving least-square (ICVMLS) approximation, a new complex variable meshless method (CVMM) for two-dimensional (2D) transient heat conduction problems is presented. The variational method is employed to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. As the transient heat conduction problems are related to time, the Crank-Nicolson difference scheme for two-point boundary value problems is selected for the time discretization. Then the corresponding formulae of the CVMM for 2D heat conduction problems are obtained. In order to demonstrate the applicability of the proposed method, numerical examples are given to show the high convergence rate, good accuracy, and high efficiency of the CVMM presented in this paper.展开更多
Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attr...Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attracted much attention and research recently. These problems are independent of time and involve only space coordinates, as in Poisson's equation or the Laplace equation with Dirichlet, Neuman, or mixed conditions. When the problems are too complex, it is difficult to find an analytical solution, the only choice left is an approximate numerical solution. This paper deals with the numerical solution of three-dimensional steady-state heat conduction problems using the meshless reproducing kernel particle method (RKPM). A variational method is used to obtain the discrete equations. The essential boundary conditions are enforced by the penalty method. The effectiveness of RKPM for three-dimensional steady-state heat conduction problems is investigated by two numerical examples.展开更多
Newton type methods are one kind of the efficient methods to solve nonlinear ill-posed problems, which have attracted extensive attention. However, computational cost of Newton type methods is high because practical p...Newton type methods are one kind of the efficient methods to solve nonlinear ill-posed problems, which have attracted extensive attention. However, computational cost of Newton type methods is high because practical problems are complicated. We propose a mixed Newton-Tikhonov method, i.e., one step Newton-Tikhonov method with several other steps of simplified Newton-Tikhonov method. Convergence and stability of this method are proved under some conditions. Numerical experiments show that the proposed method has obvious advantages over the classical Newton method in terms of computational costs.展开更多
Analytically solving a three-dimensional (3-D) bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green func...Analytically solving a three-dimensional (3-D) bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.展开更多
This paper studies to numerical solutions of an inverse heat conduction problem.The effect of algorithms based on the Newton-Tikhonov method and the Newton-implicit iterative method is investigated,and then several mo...This paper studies to numerical solutions of an inverse heat conduction problem.The effect of algorithms based on the Newton-Tikhonov method and the Newton-implicit iterative method is investigated,and then several modifications are presented.Numerical examples show the modified algorithms always work and can greatly reduce the computational costs.展开更多
On the basis of the complex variable moving least-square (CVMLS) approximation, a complex variable meshless local Petrov-Galerkin (CVMLPG) method is presented for transient heat conduction problems. The method is ...On the basis of the complex variable moving least-square (CVMLS) approximation, a complex variable meshless local Petrov-Galerkin (CVMLPG) method is presented for transient heat conduction problems. The method is developed based on the CVMLS approximation for constructing shape functions at scattered points, and the Heaviside step function is used as a test function in each sub-domain to avoid the need for a domain integral in symmetric weak form. In the construction of the well-performed shape function, the trial function of a two-dimensional (2D) problem is formed with a one-dimensional (1D) basis function, thus improving computational efficiency. The numerical results are compared with the exact solutions of the problems and the finite element method (FEM). This comparison illustrates the accuracy as well as the capability of the CVMLPG method.展开更多
The three-dimensional numerical manifold method(3D-NMM),which is based on the derivation of Galerkin's variation,is a powerful calculation tool that uses two cover systems.The 3D-NMM can be used to handle continue...The three-dimensional numerical manifold method(3D-NMM),which is based on the derivation of Galerkin's variation,is a powerful calculation tool that uses two cover systems.The 3D-NMM can be used to handle continue-discontinue problems and extend to THM coupling.In this study,we extended the 3D-NMM to simulate both steady-state and transient heat conduction problems.The modelling was carried out using the raster methods(RSM).For the system equation,a variational method was employed to drive the discrete equations,and the crucial boundary conditions were solved using the penalty method.To solve the boundary integral problem,the face integral of scalar fields and two-dimensional simplex integration were used to accurately describe the integral on polygonal boundaries.Several numerical examples were used to verify the results of 3D steady-state and transient heat-conduction problems.The numerical results indicated that the 3D-NMM is effective for handling 3D both steadystate and transient heat conduction problems with high solution accuracy.展开更多
In this paper,the authors discuss a three-dimensional problem of the semiconductor device type involved its mathematical description,numerical simulation and theoretical analysis.Two important factors,heat and magneti...In this paper,the authors discuss a three-dimensional problem of the semiconductor device type involved its mathematical description,numerical simulation and theoretical analysis.Two important factors,heat and magnetic influences are involved.The mathematical model is formulated by four nonlinear partial differential equations(PDEs),determining four major physical variables.The influences of magnetic fields are supposed to be weak,and the strength is parallel to the z-axis.The elliptic equation is treated by a block-centered method,and the law of conservation is preserved.The computational accuracy is improved one order.Other equations are convection-dominated,thus are approximated by upwind block-centered differences.Upwind difference can eliminate numerical dispersion and nonphysical oscillation.The diffusion is approximated by the block-centered difference,while the convection term is treated by upwind approximation.Furthermore,the unknowns and adjoint functions are computed at the same time.These characters play important roles in numerical computations of conductor device problems.Using the theories of priori analysis such as energy estimates,the principle of duality and mathematical inductions,an optimal estimates result is obtained.Then a composite numerical method is shown for solving this problem.展开更多
The decentralized fuzzy inference method(DFIM)is employed as an optimization technique to reconstruct time-and space-dependent heat flux of two-dimensional(2D)participating medium.The forward coupled radiative and con...The decentralized fuzzy inference method(DFIM)is employed as an optimization technique to reconstruct time-and space-dependent heat flux of two-dimensional(2D)participating medium.The forward coupled radiative and conductive heat transfer problem is solved by a combination of finite volume method and discrete ordinate method.The reconstruction task is formulated as an inverse problem,and the DFIM is used to reconstruct the unknown heat flux.No prior information on the heat flux distribution is required for the inverse analysis.All retrieval results illustrate that the time-and spacedependent heat flux of participating medium can be exactly recovered by the DFIM.The present method is proved to be more efficient and accurate than other optimization techniques.The effects of heat flux form,initial guess,medium property,and measurement error on reconstruction results are investigated.Simulated results indicate that the DFIM is robust to reconstruct different kinds of heat fluxes even with noisy data.展开更多
A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional (3D) axisymmetric continuously nonhomogeneous functionally graded materials (FGMs). Axial symmetry of geometry ...A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional (3D) axisymmetric continuously nonhomogeneous functionally graded materials (FGMs). Axial symmetry of geometry and boundary conditions reduces the original 3D initial-boundary value problem into a two-dimensional (2D) problem. Local weak forms are derived for small polygonal sub-domains which surround nodal points distributed over the cross section. In order to simplify the treatment of the essential boundary conditions, spatial variations of the temperature and heat flux at discrete time instants are interpolated by the natural neighbor interpolation. Moreover, the using of three-node triangular finite element method (FEM) shape functions as test functions reduces the orders of integrands involved in domain integrals. The semi-discrete heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. Two numerical examples are investigated and excellent results are obtained, demonstrating the potential application of the proposed approach.展开更多
The inverse heat conduction problem (IHCP) is a severely ill-posed problem in the sense that the solution ( if it exists) does not depend continuously on the data. But now the results on inverse heat conduction pr...The inverse heat conduction problem (IHCP) is a severely ill-posed problem in the sense that the solution ( if it exists) does not depend continuously on the data. But now the results on inverse heat conduction problem are mainly devoted to the standard inverse heat conduction problem. Some optimal error bounds in a Sobolev space of regularized approximation solutions for a sideways parabolic equation, i. e. , a non-standard inverse heat conduction problem with convection term which appears in some applied subject are given.展开更多
In this paper,we present a unified finite volume method preserving discrete maximum principle(DMP)for the conjugate heat transfer problems with general interface conditions.We prove the existence of the numerical solu...In this paper,we present a unified finite volume method preserving discrete maximum principle(DMP)for the conjugate heat transfer problems with general interface conditions.We prove the existence of the numerical solution and the DMP-preserving property.Numerical experiments show that the nonlinear iteration numbers of the scheme in[24]increase rapidly when the interfacial coefficients decrease to zero.In contrast,the nonlinear iteration numbers of the unified scheme do not increase when the interfacial coefficients decrease to zero,which reveals that the unified scheme is more robust than the scheme in[24].The accuracy and DMP-preserving property of the scheme are also veri ed in the numerical experiments.展开更多
Stochastic temperature distribution should be carefully inspected in the thermal-failure design of heterogeneous solids with unexpected random energy excitations.Stochastic multiscale modeling for these problems invol...Stochastic temperature distribution should be carefully inspected in the thermal-failure design of heterogeneous solids with unexpected random energy excitations.Stochastic multiscale modeling for these problems involve multiscale and highdimensional uncertain thermal parameters,which remains limitation of prohibitive computation.In this paper,we propose a multi-modes based constrained energy minimization generalized multiscale finite element method(MCEM-GMsFEM),which can transform the original stochastic multiscale model into a series of recursive multiscale models sharing the same deterministic material parameters by multiscale analysis.Thus,MCEM-GMsFEM reveals an inherent low-dimensional representation in random space,and is designed to effectively reduce the complexity of repeated computation of discretized multiscale systems.In addition,the convergence analysis is established,and the optimal error estimates are derived.Finally,several typical random fluctuations on multiscale thermal conductivity are considered to validate the theoretical results in the numerical examples.The numerical results indicate that the multi-modes multiscale approach is a robust integrated method with the excellent performance.展开更多
This paper develops a second-order multiscale asymptotic analysis and numerical algorithms for predicting heat transfer performance of porous materials with quasi-periodic structures.In these porousmaterials,they have...This paper develops a second-order multiscale asymptotic analysis and numerical algorithms for predicting heat transfer performance of porous materials with quasi-periodic structures.In these porousmaterials,they have periodic configurations and associated coefficients are dependent on the macro-location.Also,radiation effect at microscale has an important influence on the macroscopic temperature fields,which is our particular interest in this study.The characteristic of the coupled multiscale model between macroscopic scale and microscopic scale owing to quasi-periodic structures is given at first.Then,the second-ordermultiscale formulas for solving temperature fields of the nonlinear problems are constructed,and associated explicit convergence rates are obtained on some regularity hypothesis.Finally,the corresponding finite element algorithms based on multiscale methods are brought forward and some numerical results are given in detail.Numerical examples including different coefficients are given to illustrate the efficiency and stability of the computational strategy.They show that the expansions to the second terms are necessary to obtain the thermal behavior precisely,and the local and global oscillations of the temperature fields are dependent on the microscopic and macroscopic part of the coefficients respectively.展开更多
Due to the flexibility and feasibility of addressing ill-posed problems,the Bayesian method has been widely used in inverse heat conduction problems(IHCPs).However,in the real science and engineering IHCPs,the likelih...Due to the flexibility and feasibility of addressing ill-posed problems,the Bayesian method has been widely used in inverse heat conduction problems(IHCPs).However,in the real science and engineering IHCPs,the likelihood function of the Bayesian method is commonly computationally expensive or analytically unavailable.In this study,in order to circumvent this intractable likelihood function,the approximate Bayesian computation(ABC)is expanded to the IHCPs.In ABC,the high dimensional observations in the intractable likelihood function are equalized by their low dimensional summary statistics.Thus,the performance of the ABC depends on the selection of summary statistics.In this study,a machine learning-based ABC(ML-ABC)is proposed to address the complicated selections of the summary statistics.The Auto-Encoder(AE)is a powerful Machine Learning(ML)framework which can compress the observations into very low dimensional summary statistics with little information loss.In addition,in order to accelerate the calculation of the proposed framework,another neural network(NN)is utilized to construct the mapping between the unknowns and the summary statistics.With this mapping,given arbitrary unknowns,the summary statistics can be obtained efficiently without solving the time-consuming forward problem with numerical method.Furthermore,an adaptive nested sampling method(ANSM)is developed to further improve the efficiency of sampling.The performance of the proposed method is demonstrated with two IHCP cases.展开更多
In this study,an inverse-problem method was applied to estimate the solid concentration in a solid-liquid two-phase flow.An algebraic slip mixture model was introduced to solve the forward problem of solid-liquid conv...In this study,an inverse-problem method was applied to estimate the solid concentration in a solid-liquid two-phase flow.An algebraic slip mixture model was introduced to solve the forward problem of solid-liquid convective heat transfer.The time-average conservation equations of mass,momentum,energy,as well as the volume fraction equation were computed in a computational fluid dynamics(CFD)simulation.The solid concentration in the CFD model was controlled using an external program that included the inversion iteration,and an optimal estimation was performed via experimental measurements.Experiments using a fly-ash-water mixture and sand-water mixture with different solid concentrations in a horizontal pipeline were conducted to verify the accuracy of the inverse-problem method.The estimated results were rectified using a method based on the relationship between the estimated results and estimation error;consequently,the accuracy of the corrected inversion results improved significantly.After a verification through experiments,the inverse-problem method was concluded to be feasible for predicting the solid concentration,as the estimation error of the corrected results was within 7%for all experimental samples for a solid concentration of less than 50%.The inverse-problem method is expected to provide accurate predictions of the solid concentration in solid-liquid two-phase flow systems.展开更多
We consider an inverse heat conduction problem with variable coefficient on an annulus domain.In many practice applications,we cannot know the initial temperature during heat process,therefore we consider a non-charac...We consider an inverse heat conduction problem with variable coefficient on an annulus domain.In many practice applications,we cannot know the initial temperature during heat process,therefore we consider a non-characteristic Cauchy problem for the heat equation.The method of fundamental solutions is applied to solve this problem.Due to ill-posedness of this problem,we first discretize the problem and then regularize it in the form of discrete equation.Numerical tests are conducted for showing the effectiveness of the proposed method.展开更多
In this paper,we are concerned with the numerical approximation of a steady-state heat radiation problem with a nonlinear Stefan-Boltzmann boundary condition in IR^(3).We first derive an equivalent minimization probl...In this paper,we are concerned with the numerical approximation of a steady-state heat radiation problem with a nonlinear Stefan-Boltzmann boundary condition in IR^(3).We first derive an equivalent minimization problem and then present a finite element analysis to the solution of such a minimization problem.Moreover,we apply the Newton iterative method for solving the nonlinear equation resulting from the minimization problem.A numerical example is given to illustrate theoretical results.展开更多
The suppressing effect of the laser extraction on heat generation in Nd:YAG was investigated. The extraction efficiency could be deduced from the slope efficiency, and heat generation in Nd:YAG could be obtained wit...The suppressing effect of the laser extraction on heat generation in Nd:YAG was investigated. The extraction efficiency could be deduced from the slope efficiency, and heat generation in Nd:YAG could be obtained with the heat model developed, which was verified by the previous experiment. The essential reasons were given to explain the change trend of heat generation under the condition of laser extraction.展开更多
基金supported by National Natural Science Foundation of China(11101244,11271231)National Tackling Key Problems Program(20050200069)Doctorate Foundation of the Ministry of Education of China(20030422047)
文摘Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions. The electric potential is defined by an ellip- tic equation and it appears in the following three equations via the electric field intensity. The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation. A mixed finite volume element approximation, keeping physical conservation law, is used to get numerical values of the electric potential and the accuracy is improved one order. Two con- centrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences. This method can overcome numerical oscillation, dispersion and decreases computational complexity. Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened. An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations. This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.
基金Project supported by the National Natural Science Foundation of China(Grant No.11171208)the Shanghai Leading Academic Discipline Project,China(Grant No.S30106)the Innovation Fund for Graduate Student of Shanghai University of China (Grant No.SHUCX120125)
文摘In this paper, based on the improved complex variable moving least-square (ICVMLS) approximation, a new complex variable meshless method (CVMM) for two-dimensional (2D) transient heat conduction problems is presented. The variational method is employed to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. As the transient heat conduction problems are related to time, the Crank-Nicolson difference scheme for two-point boundary value problems is selected for the time discretization. Then the corresponding formulae of the CVMM for 2D heat conduction problems are obtained. In order to demonstrate the applicability of the proposed method, numerical examples are given to show the high convergence rate, good accuracy, and high efficiency of the CVMM presented in this paper.
基金supported by the Natural Science Foundation of Ningbo,China (Grant Nos.2009A610014 and 2009A610154)the Natural Science Foundation of Zhejiang Province,China (Grant No.Y6090131)
文摘Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attracted much attention and research recently. These problems are independent of time and involve only space coordinates, as in Poisson's equation or the Laplace equation with Dirichlet, Neuman, or mixed conditions. When the problems are too complex, it is difficult to find an analytical solution, the only choice left is an approximate numerical solution. This paper deals with the numerical solution of three-dimensional steady-state heat conduction problems using the meshless reproducing kernel particle method (RKPM). A variational method is used to obtain the discrete equations. The essential boundary conditions are enforced by the penalty method. The effectiveness of RKPM for three-dimensional steady-state heat conduction problems is investigated by two numerical examples.
基金supported by the Key Disciplines of Shanghai Municipality (Operations Research & Cybernetics, No. S30104)Shanghai Leading Academic Discipline Project (No. J50101)
文摘Newton type methods are one kind of the efficient methods to solve nonlinear ill-posed problems, which have attracted extensive attention. However, computational cost of Newton type methods is high because practical problems are complicated. We propose a mixed Newton-Tikhonov method, i.e., one step Newton-Tikhonov method with several other steps of simplified Newton-Tikhonov method. Convergence and stability of this method are proved under some conditions. Numerical experiments show that the proposed method has obvious advantages over the classical Newton method in terms of computational costs.
基金Project supported by the National Natural Science Foundation of China (No. 50776097)
文摘Analytically solving a three-dimensional (3-D) bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.
基金Project supported by the Key Disciplines of Shanghai Municipality (Grant No.S30104)the Shanghai Leading Academic Discipline Project (Grant No.J50101)
文摘This paper studies to numerical solutions of an inverse heat conduction problem.The effect of algorithms based on the Newton-Tikhonov method and the Newton-implicit iterative method is investigated,and then several modifications are presented.Numerical examples show the modified algorithms always work and can greatly reduce the computational costs.
基金supported by the National Natural Science Foundation of China(Grant No.51078250)the Research Project by Shanxi Scholarship Council of Shanxi Province,China(Grant No.2013-096)the Scientific&Technological Innovation Program for Postgraduates of Taiyuan University of Science and Technology,China(Grant No.20125026)
文摘On the basis of the complex variable moving least-square (CVMLS) approximation, a complex variable meshless local Petrov-Galerkin (CVMLPG) method is presented for transient heat conduction problems. The method is developed based on the CVMLS approximation for constructing shape functions at scattered points, and the Heaviside step function is used as a test function in each sub-domain to avoid the need for a domain integral in symmetric weak form. In the construction of the well-performed shape function, the trial function of a two-dimensional (2D) problem is formed with a one-dimensional (1D) basis function, thus improving computational efficiency. The numerical results are compared with the exact solutions of the problems and the finite element method (FEM). This comparison illustrates the accuracy as well as the capability of the CVMLPG method.
基金supported by the National Natural Science Foundation of China(Grant Nos.42277165,41920104007,and 41731284)the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(Grant Nos.CUGCJ1821 and CUGDCJJ202234)the National Overseas Study Fund(Grant No.202106410040)。
文摘The three-dimensional numerical manifold method(3D-NMM),which is based on the derivation of Galerkin's variation,is a powerful calculation tool that uses two cover systems.The 3D-NMM can be used to handle continue-discontinue problems and extend to THM coupling.In this study,we extended the 3D-NMM to simulate both steady-state and transient heat conduction problems.The modelling was carried out using the raster methods(RSM).For the system equation,a variational method was employed to drive the discrete equations,and the crucial boundary conditions were solved using the penalty method.To solve the boundary integral problem,the face integral of scalar fields and two-dimensional simplex integration were used to accurately describe the integral on polygonal boundaries.Several numerical examples were used to verify the results of 3D steady-state and transient heat-conduction problems.The numerical results indicated that the 3D-NMM is effective for handling 3D both steadystate and transient heat conduction problems with high solution accuracy.
基金supported by the National Natural Science Foundation of China(Grant No.11871312)Natural Science Foundation of Shandong Province(Grant No.ZR2021MA019).
文摘In this paper,the authors discuss a three-dimensional problem of the semiconductor device type involved its mathematical description,numerical simulation and theoretical analysis.Two important factors,heat and magnetic influences are involved.The mathematical model is formulated by four nonlinear partial differential equations(PDEs),determining four major physical variables.The influences of magnetic fields are supposed to be weak,and the strength is parallel to the z-axis.The elliptic equation is treated by a block-centered method,and the law of conservation is preserved.The computational accuracy is improved one order.Other equations are convection-dominated,thus are approximated by upwind block-centered differences.Upwind difference can eliminate numerical dispersion and nonphysical oscillation.The diffusion is approximated by the block-centered difference,while the convection term is treated by upwind approximation.Furthermore,the unknowns and adjoint functions are computed at the same time.These characters play important roles in numerical computations of conductor device problems.Using the theories of priori analysis such as energy estimates,the principle of duality and mathematical inductions,an optimal estimates result is obtained.Then a composite numerical method is shown for solving this problem.
基金Project supported by the Natural Science Foundation of Chongqing(CSTC,Grant No.2019JCYJ-MSXMX0441).
文摘The decentralized fuzzy inference method(DFIM)is employed as an optimization technique to reconstruct time-and space-dependent heat flux of two-dimensional(2D)participating medium.The forward coupled radiative and conductive heat transfer problem is solved by a combination of finite volume method and discrete ordinate method.The reconstruction task is formulated as an inverse problem,and the DFIM is used to reconstruct the unknown heat flux.No prior information on the heat flux distribution is required for the inverse analysis.All retrieval results illustrate that the time-and spacedependent heat flux of participating medium can be exactly recovered by the DFIM.The present method is proved to be more efficient and accurate than other optimization techniques.The effects of heat flux form,initial guess,medium property,and measurement error on reconstruction results are investigated.Simulated results indicate that the DFIM is robust to reconstruct different kinds of heat fluxes even with noisy data.
基金Project supported by the National Natural Science Foundation of China(Grant No.11002054)the Foundation of Hunan Educational Committee(Grant No.12C0059).
文摘A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional (3D) axisymmetric continuously nonhomogeneous functionally graded materials (FGMs). Axial symmetry of geometry and boundary conditions reduces the original 3D initial-boundary value problem into a two-dimensional (2D) problem. Local weak forms are derived for small polygonal sub-domains which surround nodal points distributed over the cross section. In order to simplify the treatment of the essential boundary conditions, spatial variations of the temperature and heat flux at discrete time instants are interpolated by the natural neighbor interpolation. Moreover, the using of three-node triangular finite element method (FEM) shape functions as test functions reduces the orders of integrands involved in domain integrals. The semi-discrete heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. Two numerical examples are investigated and excellent results are obtained, demonstrating the potential application of the proposed approach.
文摘The inverse heat conduction problem (IHCP) is a severely ill-posed problem in the sense that the solution ( if it exists) does not depend continuously on the data. But now the results on inverse heat conduction problem are mainly devoted to the standard inverse heat conduction problem. Some optimal error bounds in a Sobolev space of regularized approximation solutions for a sideways parabolic equation, i. e. , a non-standard inverse heat conduction problem with convection term which appears in some applied subject are given.
基金National Natural Science Foundation of China(11971069,12071045)Foundation of CAEP(CX20210042)Science Challenge Project(No.TZ2016002).
文摘In this paper,we present a unified finite volume method preserving discrete maximum principle(DMP)for the conjugate heat transfer problems with general interface conditions.We prove the existence of the numerical solution and the DMP-preserving property.Numerical experiments show that the nonlinear iteration numbers of the scheme in[24]increase rapidly when the interfacial coefficients decrease to zero.In contrast,the nonlinear iteration numbers of the unified scheme do not increase when the interfacial coefficients decrease to zero,which reveals that the unified scheme is more robust than the scheme in[24].The accuracy and DMP-preserving property of the scheme are also veri ed in the numerical experiments.
基金the Natural Science Foundation of Shanghai(No.21ZR1465800)the Science Challenge Project(No.TZ2018001)+2 种基金the Interdisciplinary Project in Ocean Research of Tongji University,the Aeronautical Science Foundation of China(No.2020001053002)the National Key R&D Program of China(No.2020YFA0713603)the Fundamental Research Funds for the Central Universities.
文摘Stochastic temperature distribution should be carefully inspected in the thermal-failure design of heterogeneous solids with unexpected random energy excitations.Stochastic multiscale modeling for these problems involve multiscale and highdimensional uncertain thermal parameters,which remains limitation of prohibitive computation.In this paper,we propose a multi-modes based constrained energy minimization generalized multiscale finite element method(MCEM-GMsFEM),which can transform the original stochastic multiscale model into a series of recursive multiscale models sharing the same deterministic material parameters by multiscale analysis.Thus,MCEM-GMsFEM reveals an inherent low-dimensional representation in random space,and is designed to effectively reduce the complexity of repeated computation of discretized multiscale systems.In addition,the convergence analysis is established,and the optimal error estimates are derived.Finally,several typical random fluctuations on multiscale thermal conductivity are considered to validate the theoretical results in the numerical examples.The numerical results indicate that the multi-modes multiscale approach is a robust integrated method with the excellent performance.
基金This work is supported by the Fundamental Research Funds for the Central Universities,the National Natural Science Foundation of China(11701123)also supported by China Postdoctoral Science Foundation(2015M580256,2016T90276).
文摘This paper develops a second-order multiscale asymptotic analysis and numerical algorithms for predicting heat transfer performance of porous materials with quasi-periodic structures.In these porousmaterials,they have periodic configurations and associated coefficients are dependent on the macro-location.Also,radiation effect at microscale has an important influence on the macroscopic temperature fields,which is our particular interest in this study.The characteristic of the coupled multiscale model between macroscopic scale and microscopic scale owing to quasi-periodic structures is given at first.Then,the second-ordermultiscale formulas for solving temperature fields of the nonlinear problems are constructed,and associated explicit convergence rates are obtained on some regularity hypothesis.Finally,the corresponding finite element algorithms based on multiscale methods are brought forward and some numerical results are given in detail.Numerical examples including different coefficients are given to illustrate the efficiency and stability of the computational strategy.They show that the expansions to the second terms are necessary to obtain the thermal behavior precisely,and the local and global oscillations of the temperature fields are dependent on the microscopic and macroscopic part of the coefficients respectively.
文摘Due to the flexibility and feasibility of addressing ill-posed problems,the Bayesian method has been widely used in inverse heat conduction problems(IHCPs).However,in the real science and engineering IHCPs,the likelihood function of the Bayesian method is commonly computationally expensive or analytically unavailable.In this study,in order to circumvent this intractable likelihood function,the approximate Bayesian computation(ABC)is expanded to the IHCPs.In ABC,the high dimensional observations in the intractable likelihood function are equalized by their low dimensional summary statistics.Thus,the performance of the ABC depends on the selection of summary statistics.In this study,a machine learning-based ABC(ML-ABC)is proposed to address the complicated selections of the summary statistics.The Auto-Encoder(AE)is a powerful Machine Learning(ML)framework which can compress the observations into very low dimensional summary statistics with little information loss.In addition,in order to accelerate the calculation of the proposed framework,another neural network(NN)is utilized to construct the mapping between the unknowns and the summary statistics.With this mapping,given arbitrary unknowns,the summary statistics can be obtained efficiently without solving the time-consuming forward problem with numerical method.Furthermore,an adaptive nested sampling method(ANSM)is developed to further improve the efficiency of sampling.The performance of the proposed method is demonstrated with two IHCP cases.
基金This study was financially supported by the National Natural Science Foundation of China(No.51679225)National Natural Sci ence Science Foundation of China(No.51706214),and China Scholarship Council.
文摘In this study,an inverse-problem method was applied to estimate the solid concentration in a solid-liquid two-phase flow.An algebraic slip mixture model was introduced to solve the forward problem of solid-liquid convective heat transfer.The time-average conservation equations of mass,momentum,energy,as well as the volume fraction equation were computed in a computational fluid dynamics(CFD)simulation.The solid concentration in the CFD model was controlled using an external program that included the inversion iteration,and an optimal estimation was performed via experimental measurements.Experiments using a fly-ash-water mixture and sand-water mixture with different solid concentrations in a horizontal pipeline were conducted to verify the accuracy of the inverse-problem method.The estimated results were rectified using a method based on the relationship between the estimated results and estimation error;consequently,the accuracy of the corrected inversion results improved significantly.After a verification through experiments,the inverse-problem method was concluded to be feasible for predicting the solid concentration,as the estimation error of the corrected results was within 7%for all experimental samples for a solid concentration of less than 50%.The inverse-problem method is expected to provide accurate predictions of the solid concentration in solid-liquid two-phase flow systems.
基金partially supported by the Natural Science Foundation of Northwest Normal University,China(No.NWNU-LKQN-17-5).
文摘We consider an inverse heat conduction problem with variable coefficient on an annulus domain.In many practice applications,we cannot know the initial temperature during heat process,therefore we consider a non-characteristic Cauchy problem for the heat equation.The method of fundamental solutions is applied to solve this problem.Due to ill-posedness of this problem,we first discretize the problem and then regularize it in the form of discrete equation.Numerical tests are conducted for showing the effectiveness of the proposed method.
文摘In this paper,we are concerned with the numerical approximation of a steady-state heat radiation problem with a nonlinear Stefan-Boltzmann boundary condition in IR^(3).We first derive an equivalent minimization problem and then present a finite element analysis to the solution of such a minimization problem.Moreover,we apply the Newton iterative method for solving the nonlinear equation resulting from the minimization problem.A numerical example is given to illustrate theoretical results.
文摘The suppressing effect of the laser extraction on heat generation in Nd:YAG was investigated. The extraction efficiency could be deduced from the slope efficiency, and heat generation in Nd:YAG could be obtained with the heat model developed, which was verified by the previous experiment. The essential reasons were given to explain the change trend of heat generation under the condition of laser extraction.