A coupled RKPM and dynamic infinite element approach for solving static and transient heat conduction problems

Abstract

A new accurate and efficient coupled method RKPM-DIEM is proposed. This is a stable and efficient meshfree nodally-integrated reproducing kernel particle method (RKPM) coupled with a dynamic infinite element method (DIEM) for solving half-space problems. The half-space domain is defined as the near field (bounded) and the far field (unbounded) analyzed by the RKPM and DIEM, respectively. Unlike the element-based methods, RKPM is constructed using only nodal data in the global Cartesian coordinates directly to avoid mesh issues such as mesh distortion and entanglement. Also, it provides flexible control of the local smoothness and order of basis, as well as easy construction for a higher-order gradient by changing the kernel function directly. DIEM is first used to show that this approach could solve not only dynamic but also static problems by setting the wave number and the decay coefficient properly. Furthermore, various meshfree integration methods, such as the Gaussian integration, the direct nodal integration, and the natural stabilized nodal integration, are tested to show accuracy and stability. Several benchmark problems are investigated to verify the effectiveness of the proposed method. It has been found that numerical results can achieve high accuracy and stability.