Adaptive simplification of complex multiscale systems

2011/03/28 by Eliodoro Chiavazzo, I. V. Karlin · 3 citations
Engineering · Physics and Astronomy · #Combustion and flame dynamics #Quantum, superfluid, helium dynamics #Advanced Thermodynamics and Statistical Mechanics

paper · pdf · doi:10.1103/physreve.83.036706

openalex publication_date 2011/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A fully adaptive methodology is developed for reducing the complexity of large dissipative systems. This represents a significant step toward extracting essential physical knowledge from complex systems, by addressing the challenging problem of a minimal number of variables needed to exactly capture the system dynamics. Accurate reduced description is achieved, by construction of a hierarchy of slow invariant manifolds, with an embarrassingly simple implementation in any dimension. The method is validated with the autoignition of the hydrogen-air mixture where a reduction to a cascade of slow invariant manifolds is observed.

Citations

• A general algorithm for improving ILDMs
• Rate-controlled partial-equilibrium method for treating reacting gas mixtures
• Quasi-equilibrium grid algorithm: Geometric construction for model reduction
• The Role of Thermodynamics in Model Reduction When Using Invariant Grids
• Approximation of Slow Attracting Manifolds in Chemical Kinetics by Trajectory-Based Optimization Approaches
• Coupling of the model reduction technique with the lattice Boltzmann method for combustion simulations
• Method of invariant manifold for chemical kinetics
• Simplifying chemical kinetics: Intrinsic low-dimensional manifolds in composition space

Cited by

• The global relaxation redistribution method for reduction of combustion kinetics
• Inference of analytical thermodynamic models for biological networks
• Combustion [wikipedia]