Microreversible collisions for polyatomic gases and Boltzmann’s theorem.(English)Zbl 0807.76067

Summary: We prove an $$H$$-theorem for two Boltzmann models describing general polyatomic gases with the help of only one additional degree of freedom. The kinetic density is then represented by a function $$f(t,x,v,I)$$, $$t \geq 0$$, $$x \in \mathbb{R}^ 3$$, $$v \in \mathbb{R}^ 3$$ and $$I \in \mathbb{R}^ +$$ where $$I^ 2$$ represents the internal energy of the particles. The first model is due to Borgnakke-Larsen, the second one is deduced from a monoatomic gas in higher dimension. Because of the nonlinearity of the microscopic collision process, the classical proof has to be adapted. These models are then illustrated by several numerical examples.

MSC:

 76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics 82B40 Kinetic theory of gases in equilibrium statistical mechanics 82D05 Statistical mechanics of gases