Meshless local Petrov-Galerkin method with moving least squares approximation for transient thermal conduction applications with variable conductivity

A numerical solution of transient 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, iii) the shape of the integration site around each node, iv) the conductivity range, and v) the 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 orthogonal-type integration sites are introduced during temporal MLPG integration, and the accuracy and the efficiency of the method are demonstrated in all cases studied.