Geometric acceleration of complex chemical equilibrium calculations — Algorithm and application to two- and three-component systems

Roos, 2022, Accelerating complex chemical equilibrium calculations - a review, CALPHAD: Comput. Coupling Phase Diagr. Thermochem., 77 Zietsman, 2006, Modelling of an ilmenite-smelting DC arc furnace process, Miner. Eng., 19, 262, 10.1016/j.mineng.2005.06.016 2019 Zietsman, 2016, Efficient storage and recall of slag thermochemical properties for use in multiphysics model, 635 A. ten Cate, B.J. Geurts, M. Muskulus, D. Koöster, A. Muntean, J. van Opheusden, A. Peschansky, B. Vreman, P. Zegeling, Modeling and Simulation of Phase-Transitions in Multicomponent Aluminum Alloy Casting, Enschede, The Netherlands, 2008, pp. 117–139. Qiu, 2015, Polynomial regression and interpolation of thermodynamic data in al-si-mg-fe system, CALPHAD: Comput. Coupling Phase Diagr. Thermochem., 48, 175, 10.1016/j.calphad.2015.01.005 Zhao, 2012, Numerical computations for temperature, fraction of solid phase and composition couplings in ternary alloy solidification with three different dhermodynamic data-acquisition methods, CALPHAD: Comput. Coupling Phase Diagr. Thermochem., 36, 155, 10.1016/j.calphad.2011.07.002 Voskov, 2008, Compositional space parametrization for miscible displacement simulation, Transp. Porous Media, 75, 111, 10.1007/s11242-008-9212-1 Voskov, 2009, Tie-simplex based mathematical framework for thermodynamical elibrium computation of mixtures with an arbitrary number of phases, Fluid Phase Equilib., 283, 1, 10.1016/j.fluid.2009.04.018 Pope, 1993 Liu, 2005, The performance of in-situ adaptive tabulation in computations of turbulent flames, Combust. Theory Model., 9, 549, 10.1080/13647830500307436 Lu, 2009, An improved algorithm for in-situ adaptive tabulation, J. Comput. Phys., 228, 361, 10.1016/j.jcp.2008.09.015 Callister, 2011 Hack, 2008, I.3 - phase diagrams, 43 Sommerville, 1929, 124 Rockafellar, 1997, 3 Van Rossum, 2009 S.K. Lam, A. Pitrou, S. Seibert, Numba: A llvm-based python jit compiler, in: Proceedings of the Second Workshop on the LLVM Compiler Infrastructure in HPC, 2015, pp. 1–6. Virtanen, 2020, Scipy 1.0: Fundamental algorithms for scientific computing in python, Nature Methods, 17, 261, 10.1038/s41592-019-0686-2