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H theorem, regularization, and boundary conditions for linearized 13 moment equations.

Henning Struchtrup¹, Manuel Torrilhon

¹ETH Zürich, Department of Materials, Polymer Physics, CH-8093 Zürich, Switzerland. struchtr@uvic.ca

Physical Review Letters

|August 7, 2007

Summary

An H theorem for linearized Grad 13 moment equations provides regularizing constitutive equations and boundary conditions. This approach accurately reproduces Couette and Poiseuille flows, matching direct simulation Monte Carlo results.

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Area of Science:

Plasma physics and rarefied gas dynamics.
Mathematical modeling of kinetic transport phenomena.

Background:

The Grad 13 moment equations are a common kinetic model for rarefied gases.
Establishing regularizing constitutive relations and complete boundary conditions is crucial for accurate solutions.

Purpose of the Study:

To develop regularizing constitutive equations and boundary conditions for linearized Grad 13 moment equations using an H theorem.
To validate the model by comparing solutions with Direct Simulation Monte Carlo (DSMC) for specific flow cases.

Main Methods:

Application of an H theorem to the linearized Grad 13 moment equations.
Derivation of regularizing constitutive relations for higher fluxes.
Formulation of a complete set of boundary conditions.
Analytical and numerical solutions for Couette and Poiseuille flows.

Main Results:

The H theorem yields regularizing constitutive equations and a complete set of boundary conditions.
Solutions for Couette and Poiseuille flows demonstrate good agreement with DSMC calculations.
The characteristic Knudsen minimum in the relative mass flow rate is successfully reproduced.

Conclusions:

The developed H theorem provides a robust framework for the linearized Grad 13 moment equations.
The regularizing constitutive equations and boundary conditions enhance the accuracy and applicability of the model.
The results validate the theoretical approach against established computational methods for rarefied gas dynamics.