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Exceptionally reliable density solving algorithms for multiparameter mixture models from Chebyshev expansion rootfinding

Published

Author(s)

Ian H. Bell, Bradley K. Alpert

Abstract

Calculation of the density of a mixture for a given tem- perature, pressure, and mixture composition from multi- parameter mixture models (like the so-called GERG model) sometimes fails; failures are caused by insuffi- ciently accurate estimations of the density root, but also by insufficiently robust numerical methods that may not converge to the desired density solution. Furthermore, generally only one density solution is located at a time. Polynomial expansions have the characteristic that all roots of the expansion can be obtained reliably. Therefore the approach we propose is to develop a very good ap- proximation to the equation of state based on Chebyshev orthogonal polynomial expansions, and explicitly solve for all the roots of the Chebyshev expansion - proxies for the roots of the equation of state. In this paper, we limit our- selves to the case where the temperature is known; the method is generalizable to other types of thermodynamic calculations. For mixtures, this Chebyshev proxy rootfinding results in a density calculation that is almost guaranteed to yield the right solution. These tools make multi-parameter equations of state nearly as reliable as cubic equations of state. The computational penalty from the use of Cheby- shev expansions can be overcome through the exploitation of parallelism, though that is not further discussed here.
Citation
Fluid Phase Equilibria

Citation

Bell, I. and Alpert, B. (2018), Exceptionally reliable density solving algorithms for multiparameter mixture models from Chebyshev expansion rootfinding, Fluid Phase Equilibria, [online], https://doi.org/10.1016/j.fluid.2018.04.026 (Accessed April 16, 2024)
Created May 21, 2018, Updated June 2, 2021