Nonlinear transient heat transfer problems using the meshfree ES-PIM

Abstract

A meshfree edge-based smoothed point interpolation method (ES-PIM) is formulated to analyze a 2-D nonlinear heat transfer problem. The nonlinearities arising from the variation of material properties and surface convection coefficients and those due to the inclusion of the radiation effects are fully considered. The PIM is used to approximate the temperature function and the thermal gradient field within edge-based smoothed domains is modified by a generalized gradient smoothing technique. To reduce the computational efforts, quasilinearization scheme is adopted to linearize the nonlinear equations, and for time integration the Euler backward method is used, as its unconditional stability allows for larger time steps. The smoothed incremental heat transfer equilibrium equations are then established using the generalized smoothed Galerkin weak form. A number of one- and two-dimensional heat transfer problems are studied in terms of the convergence in equivalent energy and the accuracy of temperature field. It is found that present ES-PIM achieves more accurate temperature results and better convergence than FEM and NS-PIM do using the same triangular background meshes and can effectively simulate complex nonlinear heat transfer problems. © Freund Publishing House Ltd., International Journal of Nonlinear Sciences & Numerical Simulation.