Transient thermal conduction with variable conductivity using the Meshless Local Petrov–Galerkin method

A numerical solution of the transient heat conduction problem with spatiotemporally vari- able conductivity in 2D space is obtained using the Meshless Local Petrov–Galerkin (MLPG) method. The approximation of the field variables is performed using Moving Least Squares (MLS) interpolation. The accuracy and the efficiency of the MLPG schemes are investigated through variation of (i) the domain resolution, (ii) the order of the basis functions, (iii) the shape of the integration site around each node, (iv) the conductivity range, and (v) the volumetric heat capacity range. Steady-state boundary conditions of the essential type are assumed. The results are compared with those calculated by a typical Finite Element method. Specific rectangular-type integration sites are introduced during both steady-state and transient MLPG integration, in order to provide complete surface coverage of the domain without overlapping, and the accuracy of the method is demonstrated in all cases studied. Computational efficiency is also investigated with this MLPG method and found to be slower than FE methods during construction stage, but it clearly surpasses that of FEM approaches during the solution stage on a wide parameter range.