An Interpolating Moving Least Squares-based meshfree approach for transient heat transfer analysis

Abstract This paper investigates a novel meshfree approach for transient heat transfer analysis of isotropic material using the Interpolating Moving Least Squares (IMLS). Building upon the strengths of meshless methods, particularly the Element-Free Galerkin (EFG) approach, the proposed method leverages the IMLS technique to construct shape functions that satisfy the Kronecker delta property, thereby allowing essential boundary conditions to be imposed directly without additional transformation or penalty methods. This significantly simplifies the numerical implementation while maintaining the flexibility and adaptability of meshfree formulations. The IMLS-based scheme is integrated within the Galerkin weak form framework to develop a robust and accurate numerical model capable of simulating transient heat transfer behavior. Unlike traditional finite element methods (FEM), which often require complex meshing procedures and suffer from accuracy issues in problems with evolving geometries of sharp gradients, the proposed meshfree method offers enhanced computational precision and geometric flexibility. The implementation is carried out in MATLAB. First, to evaluate the performance and reliability of the method, a convergence study is conducted using various nodal distributions. This analysis identified suitable node densities and support domain sizes that yield optimal accuracy and computational efficiency. The present results are then validated and verified through comparison with benchmark problems and previously published results. The numerical results demonstrate excellent agreement with the reference results, confirming the precision of the proposed IMLS-based approach. Following the validation phase, a detailed parameter sensitivity analysis was performed to investigate the influence of parameters on the temperature distribution of the structure. Finally, the method is applied to a transient heat transfer problem in a complex-shaped isotropic domain to assess its capability to handle real-world engineering problems. These findings establish a valuable benchmark for the ongoing advancement of meshfree methods and provide a solid foundation for future investigations into the applicability of methods to complex and practical engineering problems.