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Journal of Computational Physics
Article . 2025 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2023
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General numerical framework to derive structure preserving reduced order models for thermodynamically consistent reversible-irreversible PDEs

Authors: Zengyan Zhang; Jia Zhao;

General numerical framework to derive structure preserving reduced order models for thermodynamically consistent reversible-irreversible PDEs

Abstract

In this paper, we propose a general numerical framework to derive structure-preserving reduced order models for thermodynamically consistent PDEs. Our numerical framework has two primary features: (a) a systematic way to extract reduced order models for thermodynamically consistent PDE systems while maintaining their inherent thermodynamic principles and (b) a strategic process to devise accurate, efficient, and structure-preserving numerical algorithms to solve the forehead reduced-order models. The platform's generality extends to various PDE systems governed by embedded thermodynamic laws. The proposed numerical platform is unique from several perspectives. First, it utilizes the generalized Onsager principle to transform the thermodynamically consistent PDE system into an equivalent one, where the transformed system's free energy adopts a quadratic form of the state variables. This transformation is named energy quadratization (EQ). Through EQ, we gain a novel perspective on deriving reduced order models. The reduced order models derived through our method continue to uphold the energy dissipation law. Secondly, our proposed numerical approach automatically provides numerical algorithms to discretize the reduced order models. The proposed algorithms are always linear, easy to implement and solve, and uniquely solvable. Furthermore, these algorithms inherently ensure the thermodynamic laws. In essence, our platform offers a distinctive approach to derive structure-preserving reduced-order models for a wide range of PDE systems abiding by thermodynamic principles.

Related Organizations
Keywords

phase field, thermodynamically consistent, model order reduction, structure preserving, FOS: Mathematics, Initial-boundary value problems for higher-order parabolic equations, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Chemical kinetics in thermodynamics and heat transfer

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Green