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

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.