A meshless analysis of three-dimensional transient heat conduction problems

• Published in: Engineering analysis with boundary elements 2012-02, Vol.36 (2), p.203-210
• Main Authors: Cheng, R.J., Liew, K.M.
• Format: Article
• Language: English
• Subjects: Error analysis; Exact sciences and technology; Finite element method; Fundamental areas of phenomenology (including applications); Heat conduction; Heat transfer; Mathematical analysis; Mathematical models; Mathematics; Meshless method; Meshless methods; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis; Numerical analysis. Scientific computation; Numerical modeling; Partial differential equations, boundary value problems; Physics; Sciences and techniques of general use; Three dimensional; Three dimensional models; Transient heat conduction; Transient heat conduction problem; Variational methods
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/j.enganabound.2011.07.001

In this paper, we consider a numerical modeling of a three-dimensional transient heat conduction problem. The modeling is carried out using a meshless reproducing kernel particle (RKPM) method. In the mathematical formulation, a variational method is employed to derive the discrete equations. The essential boundary conditions of the formulated problems are enforced by the penalty method. Compared with numerical methods based on meshes, the RKPM needs only scattered nodes, rather than having to mesh the domain of the problem. An error analysis of the RKPM for three-dimensional transient heat conduction problem is also presented in this paper. In order to demonstrate the applicability of the proposed solution procedures, numerical experiments are carried out for a few selected three-dimensional transient heat conduction problems. ► RKPM is used to study the 3-D heat conduction problem. ► The RKPM needs only scattered nodes rather than meshes. ► Convergence of the RKPM for 3-D transient heat conduction problem is studied.