Fast explicit dynamics finite element algorithm for transient heat transfer

Abstract

This paper presents a novel methodology for fast simulation and analysis of transient heat transfer problems. The proposed methodology is suitable for real-time applications owing to (i) establishing the solution method from the viewpoint of computationally efficient explicit dynamics, (ii) proposing an element-level thermal load computation to eliminate the need for assembling global thermal stiffness matrix, leading to (iii) an explicit formulation of nodal temperature computation to eliminate the need for iterations anywhere in the algorithm, (iv) pre-computing the constant matrices and simulation parameters to facilitate online calculation, and (v) utilising computationally efficient finite elements to efficiently obtain thermal responses in the spatial domain, all of which lead to a significant reduction in computation time for fast run-time simulation. The proposed fast explicit dynamics finite element algorithm (FED-FEM) employs nonlinear thermal material properties, such as temperature-dependent thermal conductivity and specific heat capacity, and nonlinear thermal boundary conditions, such as heat convection and radiation, to account for the nonlinear characteristics of transient heat transfer problems. Simulations and comparison analyses demonstrate that not only can the proposed methodology handle isotropic, orthotropic, anisotropic and temperature-dependent thermal properties but also satisfy the standard patch tests and achieve good agreement with those of the commercial finite element analysis packages for numerical accuracy, for three-dimensional (3-D) heat conduction, convection, radiation, and thermal gradient concentration problems. Furthermore, the proposed FED-FEM algorithm is computationally efficient and only consumes a small computation time, capable of achieving real-time computational performance, leading to a novel methodology suitable for real-time simulation and analysis of transient heat transfer problems.