Application of Generalized (Hyper-) Dual Numbers in Equation of State Modeling
Philipp Rehner, Gernot Bauer
Abstract
The calculation of derivatives is ubiquitous in science and engineering. In thermodynamics, in particular, state properties can be expressed as derivatives of thermodynamic potentials. The manual differentiation of complex models can be tedious and error-prone. In this work, we revisit dual and hyper-dual numbers for the calculation of exact derivatives and show generalizations to higher order derivatives and derivatives with respect to vector quantities. The methods described in this paper are accompanied by an open source Rust implementation with Python bindings. Applications of the generalized (hyper-) dual numbers are given in the context of equation of state modeling and the calculation of critical points.
Topics & Concepts
Python (programming language)Dual (grammatical number)Automatic differentiationApplied mathematicsContext (archaeology)Computer scienceMathematicsAlgebra over a fieldAlgorithmPure mathematicsProgramming languagePaleontologyBiologyArtComputationLiteraturePhase Equilibria and ThermodynamicsAdvanced Thermodynamics and Statistical MechanicsProcess Optimization and Integration