Fast explicit dynamics finite element algorithm for transient heat transfer

Transient heat transfer plays a significant role in numerous engineering applications. Its analysis is mainly achieved based on numerical methods. Engineering applications nowadays demand more realistic and real-time solutions of transient heat transfer problems. As such, numerical methods are developed to focus not only on the accuracy, convergence and stability but also on the computation time to justify the conflicting requirements (realistic and real-time).

While transient heat transfer problems may have nonlinear characteristics due to nonlinear heat transfer behaviors and the influence of time and temperature on the material characteristics, finite element-based methods are generally computationally expensive for nonlinear problems. Recently, a reduced-order modeling concept was introduced to enhance the computational performance of the finite element method. Despite the improvement in numerical efficiency, the accuracy of the algorithm is limited by the chosen reduced-basis.

Researchers: Dr. Jinao Zhang and Professor Sunita Chauhan from the Department of Mechanical and Aerospace Engineering, Monash University, Australia, presented a new interesting approach for fast simulation and analysis of transient heat transfer problems. To ensure fast and efficient numerical updates in the run-time computation, the proposed methodology entailed: establishing the solution procedure based on the computationally efficient explicit dynamics, eliminating the need for assembling nonlinear global thermal stiffness matrix by employing an element-level thermal load computational approach, and eliminating the need for iterative solution procedure in the algorithm. This approach employed nonlinear thermal material properties as well as nonlinear thermal boundary conditions to account for the observed nonlinear characteristics of the transient heat transfer problems. The work is published in International Journal of Thermal Sciences.

These contributions lead to an efficient explicit formulation for calculating the nodal temperature by determining the nonlinear nodal thermal loads at the element level from the finite elements sharing the node. Furthermore, pre-computation of simulation parameters like nodal spatial derivatives and time-stepping constants was made possible. From the simulations and comparative analyses, the authors observed that the method could handle isotropic, orthotropic, anisotropic as well as temperature-dependent thermal properties. Besides, the standard patch tests produced results with good agreements with the analytical solutions, and simulated results are compared against those from commercial finite element analysis for numerical accuracy for radiation, conduction, convection, and thermal gradient concentration problems.

The fast explicit dynamics finite element algorithm is computationally efficient and saves time as compared to conventional algorithms. For instance, simulation parameters can be pre-computed offline before online simulation thus improving the computational performance of the results. In addition, it does not require nonlinear global thermal matrices assembly and iterative solutions in the algorithm; the treatment of nonlinear boundary conditions is straightforward, and nodal equations are independent which are well suited for parallel computing.

According to the authors, the proposed algorithm is capable of achieving real-time computational performance for real-time simulation of transient heat transfer problems. This includes a multi-thread CPU implementation and potential GPU parallel implementation by independently computing the unknown individual nodal temperature. The study by Dr. Jinao Zhang and Professor Sunita Chauhan has laid the foundation for improved future fast explicit dynamics finite element algorithms.