A closed-box kernel function for numerical simulation of transient heat conduction

A new kernel function, termed the closed-box kernel function, has been developed to address numerical simulation of transient heat conduction in the same medium. Firstly, this method is versatile and not limited to specific industrial scenarios or designated materials. Secondly, the method solves the spatial temperature at each time point only once, eliminating the need for multiple iterations. Thirdly, the method allows for controlled and adjustable simulation speed of heat conduction while maintaining high accuracy. After 24,700 iterations in the transient process, the relative error in temperature values is merely 0.000072. Fourthly, this numerical technique can break data dependency between spatial nodes, making it suitable for parallel computing with Graphics Processing Units (GPUs). The average speedup achieved is 94.0712 times faster compared to Central Processing Unit (CPU) computations. Finally, we provide mathematical examples to verify the correctness and accuracy of this numerical approach and present a computational framework for parallel computing in the Visual Studio (VS) programming environment to demonstrate its practicality in engineering applications.