The numerical manifold method(NMM)introduces the mathematical and physical cover to solve both continuum and discontinuum problems in a unified manner.In this study,the NMM for solving steady-state nonlinear heat cond...The numerical manifold method(NMM)introduces the mathematical and physical cover to solve both continuum and discontinuum problems in a unified manner.In this study,the NMM for solving steady-state nonlinear heat conduction problems is presented,and heat conduction problems consider both convection and radiation boundary conditions.First,the nonlinear governing equation of thermal conductivity,which is dependent on temperature,is transformed into the Laplace equation by introducing the Kirchhoff transformation.The transformation reserves linearity of both the Dirichlet and the Neumann boundary conditions,but the Robin and radiation boundary conditions remain nonlinear.Second,the NMM is employed to solve the Laplace equation using a simple iteration procedure because the nonlinearity focuses on parts of the problem domain boundaries.Finally,the temperature field is retrieved through the inverse Kirchhoff transformation.Typical examples are analyzed,demonstrating the advantages of the Kirchhoff transformation over the direct solution of nonlinear equations using the NewtonRaphson method.This study provides a new method for calculating nonlinear heat conduction.展开更多
Accurately solving transient nonlinear inverse heat conduction problems in complex structures is of great importance to provide key parameters for modeling coupled heat transfer process and the structure’s optimizati...Accurately solving transient nonlinear inverse heat conduction problems in complex structures is of great importance to provide key parameters for modeling coupled heat transfer process and the structure’s optimization design.The finite element method in ABAQUS is employed to solve the direct transient nonlinear heat conduction problem.Improved particle swarm optimization(PSO)method is developed and used to solve the transient nonlinear inverse problem.To investigate the inverse performances,some numerical tests are provided.Boundary conditions at inaccessible surfaces of a scramjet combustor with the regenerative cooling system are inversely identified.The results show that the new methodology can accurately and efficiently determine the boundary conditions in the scramjet combustor with the regenerative cooling system.By solving the transient nonlinear inverse problem,the improved particle swarm optimization for solving the transient nonlinear inverse heat conduction problem in a complex structure is verified.展开更多
The steady-state heat conduction in heat conductors with temperature dependent thermal conductivity and mixed boundary conditions involving radiation is investigated using the method of fundamental solutions.Various c...The steady-state heat conduction in heat conductors with temperature dependent thermal conductivity and mixed boundary conditions involving radiation is investigated using the method of fundamental solutions.Various computational issues related to the method are addressed and numerical results are presented and discussed for problems in two and three dimensions.展开更多
EQrot nonconforming finite element approximation to a class of nonlinear dual phase lagging heat conduction equations is discussed for semi-discrete and fully-discrete schemes. By use of a special property, that is, t...EQrot nonconforming finite element approximation to a class of nonlinear dual phase lagging heat conduction equations is discussed for semi-discrete and fully-discrete schemes. By use of a special property, that is, the consistency error of this element is of order O（h2） one order higher than its interpolation error O（h）, the superclose results of order O（h2） in broken Hi-norm are obtained. At the same time, the global superconvergence in broken Hi-norm is deduced by interpolation postprocessing technique. Moreover, the extrapolation result with order O（h4） is derived by constructing a new interpolation postprocessing operator and extrapolation scheme based on the known asymptotic expansion formulas of EQrot element. Finally, optimal error estimate is gained for a proposed fully-discrete scheme by different approaches from the previous literature.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.52079002 and 52130905)。
文摘The numerical manifold method(NMM)introduces the mathematical and physical cover to solve both continuum and discontinuum problems in a unified manner.In this study,the NMM for solving steady-state nonlinear heat conduction problems is presented,and heat conduction problems consider both convection and radiation boundary conditions.First,the nonlinear governing equation of thermal conductivity,which is dependent on temperature,is transformed into the Laplace equation by introducing the Kirchhoff transformation.The transformation reserves linearity of both the Dirichlet and the Neumann boundary conditions,but the Robin and radiation boundary conditions remain nonlinear.Second,the NMM is employed to solve the Laplace equation using a simple iteration procedure because the nonlinearity focuses on parts of the problem domain boundaries.Finally,the temperature field is retrieved through the inverse Kirchhoff transformation.Typical examples are analyzed,demonstrating the advantages of the Kirchhoff transformation over the direct solution of nonlinear equations using the NewtonRaphson method.This study provides a new method for calculating nonlinear heat conduction.
基金supported by the National Natural Science Foundation of China(Nos.12172078,51576026)Fundamental Research Funds for the Central Universities in China(No.DUT21LK04)。
文摘Accurately solving transient nonlinear inverse heat conduction problems in complex structures is of great importance to provide key parameters for modeling coupled heat transfer process and the structure’s optimization design.The finite element method in ABAQUS is employed to solve the direct transient nonlinear heat conduction problem.Improved particle swarm optimization(PSO)method is developed and used to solve the transient nonlinear inverse problem.To investigate the inverse performances,some numerical tests are provided.Boundary conditions at inaccessible surfaces of a scramjet combustor with the regenerative cooling system are inversely identified.The results show that the new methodology can accurately and efficiently determine the boundary conditions in the scramjet combustor with the regenerative cooling system.By solving the transient nonlinear inverse problem,the improved particle swarm optimization for solving the transient nonlinear inverse heat conduction problem in a complex structure is verified.
文摘The steady-state heat conduction in heat conductors with temperature dependent thermal conductivity and mixed boundary conditions involving radiation is investigated using the method of fundamental solutions.Various computational issues related to the method are addressed and numerical results are presented and discussed for problems in two and three dimensions.
基金Supported by the National Natural Science Foundation of China (Nos. 10971203 11101381)+3 种基金Tianyuan Mathe-matics Foundation of National Natural Science Foundation of China (No. 11026154)Natural Science Foundation of Henan Province (No. 112300410026)Natural Science Foundation of the Education Department of Henan Province (Nos. 2011A110020 12A110021)
文摘EQrot nonconforming finite element approximation to a class of nonlinear dual phase lagging heat conduction equations is discussed for semi-discrete and fully-discrete schemes. By use of a special property, that is, the consistency error of this element is of order O（h2） one order higher than its interpolation error O（h）, the superclose results of order O（h2） in broken Hi-norm are obtained. At the same time, the global superconvergence in broken Hi-norm is deduced by interpolation postprocessing technique. Moreover, the extrapolation result with order O（h4） is derived by constructing a new interpolation postprocessing operator and extrapolation scheme based on the known asymptotic expansion formulas of EQrot element. Finally, optimal error estimate is gained for a proposed fully-discrete scheme by different approaches from the previous literature.
