On choosing a nonlinear initial iterate for solving the 2-D 3-T heat conduction equations

  • Authors:

  • Heng-Bin An;Ze-Yao Mo;Xiao-Wen Xu;Xu Liu

  • Affiliations:

  • High Performance Computing Center, Institute of Applied Physics and Computational Mathematics, Beijing 100088, PR China;High Performance Computing Center, Institute of Applied Physics and Computational Mathematics, Beijing 100088, PR China;High Performance Computing Center, Institute of Applied Physics and Computational Mathematics, Beijing 100088, PR China;Graduate School of China Academy of Engineering Physics, Beijing 100088, PR China

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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Abstract

The 2-D 3-T heat conduction equations can be used to approximately describe the energy broadcast in materials and the energy swapping between electron and photon or ion. To solve the equations, a fully implicit finite volume scheme is often used as the discretization method. Because the energy diffusion and swapping coefficients have a strongly nonlinear dependence on the temperature, and some physical parameters are discontinuous across the interfaces between the materials, it is a challenge to solve the discretized nonlinear algebraic equations. Particularly, as time advances, the temperature varies so greatly in the front of energy that it is difficult to choose an effective initial iterate when the nonlinear algebraic equations are solved by an iterative method. In this paper, a method of choosing a nonlinear initial iterate is proposed for iterative solving this kind of nonlinear algebraic equations. Numerical results show the proposed initial iterate can improve the computational efficiency, and also the convergence behavior of the nonlinear iteration.