A rapid GPU-based heat transfer and solidification model for dynamic computer simulations of continuous steel casting

The paper presents a GPU-based model for continuous casting of steel. The model provides rapid computation capabilities required for real-time use in the casting control and optimization. The fully three-dimensional formulation of the heat transfer and solidification model is based on the control volume method and it allows for very fast transient simulations of the thermal behaviour of cast strands. The developed model has been verified on Stefan problem and validated with industry measurements. Heat transfer conditions in the mould and secondary cooling were determined experimentally in lab-scale experiments. The computational model is implemented as highly-parallel with the use of the NVIDIA CUDA architecture, which enables to launch the model on graphics processing units (GPUs) allowing for its great acceleration. The acceleration can be evaluated with the use of the relative computational time, which is the dimensionless ratio between the computational time that the model needs to compute the simulation and the wall-clock time of the real casting process being simulated. The relative computational time of the presented GPU-based computational model is between 0.0016 for a coarse mesh and 0.27 for a very fine mesh. The corresponding multiple of the GPU-acceleration, which is the ratio between the computational time of the GPU-based model and of the CPU-based model for the identical simulation, is between 33 and 68.