Boundary function method for boundary identification in two-dimensional steady-state nonlinear heat conduction problems

摘要

In this article, a novel meshless boundary function method (BFM) is proposed for solving the boundary identification problem of steady-state nonlinear heat conduction in arbitrary plane domain. Firstly, the original governing equation is transformed to a new one with homogeneous Cauchy boundary conditions by using a homogenization technique. Secondly, the domain type meshless collocation method is employed to solve the new partial different equation in a reduced domain, in which the numerical solution is expanded by a sequence of boundary functions, automatically satisfying the homogeneous boundary conditions on the known boundary. After that, a nonlinear equation corresponding to each angle is formed and then is solved by the Newton iterative method in order to determine the missing boundary shape. Finally, the accuracy and robustness of the proposed BFM are examined through three numerical examples.