Entropy-Related Extremum Principles for Model Reduction of Dissipative Dynamical Systems

2010/04/01 by Dirk Lebiedz · 1 citation
Engineering · Chemical Engineering · #Combustion and flame dynamics #Heat transfer and supercritical fluids #Advanced Combustion Engine Technologies

paper · pdf · doi:10.3390/e12040706

openalex publication_date 2010/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22

Abstract

Chemical kinetic systems are modeled by dissipative ordinary differential equations involving multiple time scales. These lead to a phase flow generating anisotropic volume contraction. Kinetic model reduction methods generally exploit time scale separation into fast and slow modes, which leads to the occurrence of low-dimensional slow invariant manifolds. The aim of this paper is to review and discuss a computational optimization approach for the numerical approximation of slow attracting manifolds based on entropy-related and geometric extremum principles for reaction trajectories.

Citations

• CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
• Rate-controlled partial-equilibrium method for treating reacting gas mixtures
• Quasi-equilibrium grid algorithm: Geometric construction for model reduction
• Approximation of Slow Attracting Manifolds in Chemical Kinetics by Trajectory-Based Optimization Approaches
• On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
• Simplifying chemical kinetics: Intrinsic low-dimensional manifolds in composition space

Cited by

• Combustion [wikipedia]