Model-error estimation and model adaptivity for hyperbolic moment equations in one dimension
Rik Verbiest1, Julian Koellermeier1,2
1Bernoulli Institute, University of Groningen, Nijenborgh 9, Groningen, 9747 AG The Netherlands.
Microfluidics and Nanofluidics
|July 19, 2026
Summary
This study introduces adaptive moment models for rarefied gas microflows. The new models efficiently capture varying gas rarefaction, achieving accurate results and significant computational speedups.
Area of Science:
- Fluid dynamics
- Computational physics
Background:
- Microflows often involve rarefied gases with varying degrees of rarefaction.
- Modeling these gases requires adaptive approaches to handle different complexities efficiently.
Purpose of the Study:
- To develop space- and time-adaptive moment models for rarefied gas microflows.
- To enable efficient and accurate simulation of microflows with heterogeneous rarefaction.
Main Methods:
- Derived analytical model-error estimators for Hyperbolic Moment Equations (HME) models.
- Implemented a domain decomposition strategy with varying HME model orders.
- Adapted a padded buffer cell approach for coupling different-order HME models within a finite volume scheme.
Main Results:
- The adaptive moment model successfully captures varying rarefaction degrees in microflows.
- Numerical results show accuracy comparable to validated DVM benchmark data.
- Achieved computational speedups of up to 40% compared to uniform high-order models.
Conclusions:
- The proposed adaptive moment model offers an efficient and accurate solution for simulating rarefied gas microflows.
- This approach effectively handles complex flow fields with varying gas rarefaction.
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