Efficiency of the meshless local Petrov-Galerkin method with moving least squares approximation for thermal conduction applications

A numerical solution of steady-state heat conduction problem with variable conductivity in 2D space is obtained using the meshless local Petrov-Galerkin (MLPG) method. The essential boundary condition is enforced by the transformation 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, and iii) the conductivity range. Steady-state boundary conditions of the essential type are assumed. The results are compared with those calculated by typical Finite Element, Finite Difference, and Lattice-Boltzmann Methods. Appropriate combination of the 1 ^st and the 2^nd order basis functions is proposed (hybrid order), and the accuracy and the efficiency of the method are demonstrated in all cases studied.