Numerical Modelling Of Direct/Inverse/Interval Hyperbolic Heat Transfer Problems Via TPAA-SBFE

The hyperbolic heat conduction equation is used to describe the heat transfer problem involving non-Fourier effect,its numerical solution has important practical application value and theoretical significance.Based on the temporally piecewise adaptive method(TPAA)and the scaled boundary finite element method(SBFEM),the research on the numerical solution method of the deterministic / uncertain hyperbolic heat conduction problem is carried out in this paper.The main work includes:(1)For the deterministic direct hyperbolic heat conduction problem,a numerical solution method based on the temporally piecewise adaptive method and the scaled boundary element method is proposed.By separating variables piecewisely,the spatiotemporal hyperbolic heat conduction problem is decoupled into a series of spatial problems,and the scaled boundary element method is used to discrete the solution domain and get the numerical solution.By applying an adaptive calculation in the time domain,the proposed method can maintain stable calculation accuracy when the step size changes,and there are no requirements of additional assumptions or iterative calculations for problems with nonlinear radiation boundary conditions.And it is convenient to calculate the relevant temperature derivatives adaptively.(2)For the interval direct hyperbolic heat conduction,a numerical solution method based on sensitivity analysis,Taylor expansion,interval algorithm is proposed and the adaptive calculation formula of temperature derivative is derived.Then based on the first-order/second-order Taylor approximation,a model for estimating upper and lower bounds of temperature field is established.When the thermal physical parameters and boundary conditions have interval uncertainties,the upper and lower bounds of the temperature field can be determined.(3)For the inverse hyperbolic heat conduction problem,a numerical solution method based on sensitivity analysis is proposed.The calculation accuracy of the direct problem solution and related sensitivity analysis in the inverse problem is ensured by adaptive calculation.L-M algorithm is used to solve the optimization problem related to the inverse problem,and the impacts of initial guess,number of measurement points and noise data on the results are considered.(4)Several numerical examples are given to verify the effectiveness of the above algorithm.