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Quasi-Newton Single-Phase Stability Testing without Explicit Hessian Calculation

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Abstract

A robust algorithm (solver) for testing the single-phase stability of a multicomponent fluid under isochoric-isobaric conditions is developed. The approach is based on the quasi-Newton minimization of Helmholtz free energy. The solver does not need explicit Hessian calculation when used with properly scaled variables. The solver is not tied to a specific equation of state and is applicable when the derivatives are calculated using automatic differentiation. The generation of initial estimates only needs an auxiliary cubic equation of state. We analyze the robustness and performance of the solver and present calculations of the phase boundary for a number of mixtures using the cubic equation of state and the equation of state from the family of the statistical association fluid theory (SAFT).

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Funding

The solvers were developed with the support of the Russian Science Foundation (project 17-79-20391).

The performance analysis was supported by the Ministry of Science and Higher Education of the Russian Federation (State Assignment No. 075-01056-22-00).

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Authors and Affiliations

  1. Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow Institute of Physics and Technology (National Research University), Moscow, Russia

    S. A. Zakharov & V. V. Pisarev

Authors
  1. S. A. Zakharov
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  2. V. V. Pisarev
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Correspondence to S. A. Zakharov or V. V. Pisarev.

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Zakharov, S.A., Pisarev, V.V. Quasi-Newton Single-Phase Stability Testing without Explicit Hessian Calculation. Math Models Comput Simul 15, 894–904 (2023). https://doi.org/10.1134/S2070048223050137

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  • DOI: https://doi.org/10.1134/S2070048223050137

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