Accelerated Method for Simulating the Solidification Microstructure of Continuous Casting Billets on GPUs

. 2025 Apr 25;18(9):1955. doi: 10.3390/ma18091955

Algorithm 2. Two methods for solute diffusion coefficient and interface normal angle.

\begin{array}{l} n a i v e v e r s i o n \\ coeiffocient of solute diffusion \\ 1 . i f (f_{s} = = 1) t h e n \\ 2 . D = 0; \\ 3 . e l s e \\ 4 . D = f_{s} D_{s} + (1 - f_{s}) D_{l}; \\ 5 . e n d i f \\ interface normal angle \\ 6 . i f (\partial_{x} f_{s} > 0) t h e n \\ 7 . angle = acos (\partial_{x} f_{s} / sqrt (\partial_{x} {f_{s}}^{2} + \partial_{y} {f_{s}}^{2})) \\ 8 . e l s e i f (\partial_{x} f_{s} | | \partial_{y} f_{s}) \\ 9 . angle = 2 π - acos (- \partial_{x} f_{s} / sqrt (\partial_{x} {f_{s}}^{2} + \partial_{y} {f_{s}}^{2})) \\ 10 . e n d i f \end{array} \begin{array}{l} r e d e s i g n e d v e r s i o n \\ coeiffocient of solute diffusion \\ D = (f_{s} = = 1) \cdot 0 + (f_{s} < 1) \cdot (f_{s} D_{s} + (1 - f_{s}) D_{l}); \\ interface normal angle \\ angle = (\partial_{x} f_{s} > 0) \cdot acos (\partial_{x} f_{s} / sqrt (\partial_{x} {f_{s}}^{2} + \partial_{y} {f_{s}}^{2})) + (\partial_{x} f_{s} \geq 0 \\ && (\partial_{x} f_{s} | | \partial_{y} f_{s})) \cdot (2 π - acos (- \partial_{x} f_{s} / sqrt (\partial_{x} {f_{s}}^{2} + \partial_{y} {f_{s}}^{2}))) \end{array}