MLPG analysis of Nonlinear Heat Conduction in Irregular Domains

MLPG method is a meshfree method which removes the need of meshing of computational domain at any stage of numerical analysis. Current article extends MLPG method to nonlinear heat conduction in irregular domains including the problem of solid-liquid phase change. Moving least square (MLS) scheme is used to interpolate the trial function and a fourth order spline function is used as the test function. Method of direct interpolation is used to enforce essential boundary conditions. Nonlinearities in the problems are handled with an iterative predictor-corrector method. Time integration is performed using theta-method. MLPG method has also been extended to non-homogeneous heat conduction. MLPG results are found to be in a good agreement with available exact solution/FEM results.