CND-14-1233, WU, Page 1 / 8 Computing schemes for longitudinal train dynamics: sequential, parallel and hybrid Qing Wu Centre for Railway Engineering, Central Queensland University, QLD4701, Australia. e-mail: q.wu@cqu.edu.au Colin Cole Centre for Railway Engineering, Central Queensland University, QLD4701, Australia. e-mail: c.cole@cqu.edu.au This is a self-archiving version; minor differences may exist with the published version. Qing Wu, Colin Cole (2015): Computing schemes for longitudinal train dynamics: sequential, parallel and hybrid, Journal of Computational and Nonlinear Dynamics, doi:10.1115/1.4029716 Conventionally, force elements in longitudinal train dynamics (LTD) are determined sequentially. Actually, all these force elements are independent from each other, i.e., determination of each one does not require inputs from others. This independent feature makes LTD feasible for parallel computing. A parallel scheme has been proposed and compared with the conventional sequential scheme in regard to computational efficiency. The parallel scheme is tested as not suitable for LTD; computing time of the parallel scheme is about 165% of the sequential scheme on a four-CPU personal computer (PC). A modified parallel scheme named the hybrid scheme was then proposed. The computing time of the hybrid scheme is only 70% of the sequential scheme. The other advantage of the hybrid scheme is that only two processors are required, which means the hybrid scheme can be implemented on PCs. Keywords: parallel computing, hybrid computing, longitudinal train dynamics, computational efficiency 1 Introduction LTD is a critical issue for understanding the operations of heavy haul trains. As the demand for mining industry and transport for raw materials continues to grow, freight trains are evolving to heavier, longer and faster configurations. Simulation studies of long train systems will continue to be required. Though LTD studies have been simplified by the single degree of freedom assumption, which means only the longitudinal freedom is considered for each vehicle; the complexity of LTD is still universally acknowledged [1]. Conventionally, in computing of LTD, all force elements (traction forces, in-train forces, etc.) are determined sequentially, and then velocities and locations of all vehicles are updated by using a numerical solver. Due to the sequential feature of the conventional computing scheme, it is called the sequential scheme. With advancements from both hardware and algorithm aspects; real-time LTD simulations (e.g., 210 wagons, detailed models, fourth Runge-Kutta solver with the step-size of 10E-4 second) by using the sequential scheme are already achieved. Real-time simulations have met the requirements of train driving simulators that are being used to train drivers; as well as the requirements of studies that do not need to simulate very long trips or many long trips. Recent years, a new type of simulation scenario is frequently mentioned: whole-trip or long-trip simulations [2]. A whole-trip simulation uses full-length track information (curvatures, gradients, and speed limits), train information (rolling stock types and train configurations) and control information (traction and brake) to simulate the train running from the departure station to