2 research outputs found
On a Positive decomposition of entropy production functional for the polyatomic BGK model
In this paper, we show that the entropy production functional for the
polyatomic ellipsoidal BGK model can be decomposed into two non-negative parts.
Two applications of this property: the -theorem for the polyatomic BGK model
and the weak compactness of the polyatomic ellipsoidal relaxation operator, are
discussed
Stationary Flows of the ES-BGK model with the correct Prandtl number
Ellipsoidal BGK model (ES-BGK) is a generalized version of the BGK model
where the local Maxwellian in the relaxation operator of the BGK model is
extended to an ellipsoidal Gaussian with a Prandtl parameter , so that the
correct transport coefficients can be computed in the Navier-Stokes limit. In
this work, we consider the existence and uniqueness of stationary solutions for
the ES-BGK model in a slab imposed with the mixed boundary conditions. One of
the key difficulties arise in the uniform control of the temperature tensor
from below. In the non-critical case , we utilize the property
that the temperature tensor is equivalent to the temperature in this range. In
the critical case, , where such equivalence relation breaks down,
we observe that the size of bulk velocity in direction can be controlled by
the discrepancy of boundary flux, which enables one to bound the temperature
tensor from below