Application of Generalized (Hyper-) Dual Numbers in Equation of State Modeling
Application of Generalized (Hyper-) Dual Numbers in Equation of State Modeling
复制标题
广义（超）对偶数在状态方程建模中的应用
DOI：
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发表时间：
2021
影响因子：
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通讯作者：
G. Bauer
中科院分区：
文献类型：
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作者：
Philipp Rehner;G. Bauer
导数的计算在科学和工程中是普遍存在的。特别是在热力学中，状态性质可以表示为热力学势的导数。复杂模型的手动微分可能是繁琐且容易出错的。在这项工作中，我们重新审视对偶和超对偶数的精确导数的计算，并显示概括高阶导数和导数相对于向量量。本文中描述的方法附带了一个带有Python绑定的开源Rust实现。广义（超）对偶数的应用给出的状态方程建模和临界点的计算的背景下。
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.