Based on the traditional finite volume method, a new numerical technique is presented for the transient temperature field prediction with interval uncertainties in both the physical parameters and initial/boundary con...Based on the traditional finite volume method, a new numerical technique is presented for the transient temperature field prediction with interval uncertainties in both the physical parameters and initial/boundary conditions. New stability theory applicable to interval discrete schemes is developed. Interval ranges of the uncertain temperature field can be approximately yielded by two kinds of parameter perturbation methods. Different order Neumann series are adopted to approximate the interval matrix inverse. By comparing the results with traditional Monte Carlo simulation, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed model and methods.展开更多
Based on the combination of stochastic mathematics and conventional finite difference method,a new numerical computing technique named stochastic finite difference for solving heat conduction problems with random phys...Based on the combination of stochastic mathematics and conventional finite difference method,a new numerical computing technique named stochastic finite difference for solving heat conduction problems with random physical parameters,initial and boundary conditions is discussed.Begin with the analysis of steady-state heat conduction problems,difference discrete equations with random parameters are established,and then the computing formulas for the mean value and variance of temperature field are derived by the second-order stochastic parameter perturbation method.Subsequently,the proposed random model and method are extended to the field of transient heat conduction and the new analysis theory of stability applicable to stochastic difference schemes is developed.The layer-by-layer recursive equations for the first two probabilistic moments of the transient temperature field at different time points are quickly obtained and easily solved by programming.Finally,by comparing the results with traditional Monte Carlo simulation,two numerical examples are given to demonstrate the feasibility and effectiveness of the presented method for solving both steady-state and transient heat conduction problems.展开更多
基金supported by the National Special Fund for Major Research Instrument Development(Grant No.2011YQ140145)111 Project(Grant No.B07009)+1 种基金National Natural Science Foundation of China(Grant No.11002013)Defense Industrial Technology Development Program(Grant Nos.A2120110001 and B2120110011)
文摘Based on the traditional finite volume method, a new numerical technique is presented for the transient temperature field prediction with interval uncertainties in both the physical parameters and initial/boundary conditions. New stability theory applicable to interval discrete schemes is developed. Interval ranges of the uncertain temperature field can be approximately yielded by two kinds of parameter perturbation methods. Different order Neumann series are adopted to approximate the interval matrix inverse. By comparing the results with traditional Monte Carlo simulation, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed model and methods.
基金supported by the National Natural Science Foundation of China(Grant Nos.90816024,10872017 and 10876100)the Defense Industrial Technology Development Program(Grant Nos.A2120110001 and B2120110011)the 111 Project(Grant No.B07009)
文摘Based on the combination of stochastic mathematics and conventional finite difference method,a new numerical computing technique named stochastic finite difference for solving heat conduction problems with random physical parameters,initial and boundary conditions is discussed.Begin with the analysis of steady-state heat conduction problems,difference discrete equations with random parameters are established,and then the computing formulas for the mean value and variance of temperature field are derived by the second-order stochastic parameter perturbation method.Subsequently,the proposed random model and method are extended to the field of transient heat conduction and the new analysis theory of stability applicable to stochastic difference schemes is developed.The layer-by-layer recursive equations for the first two probabilistic moments of the transient temperature field at different time points are quickly obtained and easily solved by programming.Finally,by comparing the results with traditional Monte Carlo simulation,two numerical examples are given to demonstrate the feasibility and effectiveness of the presented method for solving both steady-state and transient heat conduction problems.
