On the comparison between phenomenological and kinetic theories of gas mixtures with applications to flocking
arxiv(2024)
摘要
We study the compression between the phenomenological and kinetic models for
a mixture of gases from the viewpoint of collective dynamics. In the case in
which constituents are Eulerian gases, balance equations for mass, momentum,
and energy are the same in the main differential part, but production terms due
to the interchanges between constituents are different. They coincide only when
the thermal and mechanical diffusion are sufficiently small. In this paper, we
first verify that both models satisfy the universal requirements of
conservation laws of total mass, momentum, and energy, Galilean invariance and
entropy principle. Following the work of Ha and Ruggeri (ARMA 2017), we
consider spatially homogeneous models which correspond to the generalizations
of the Cucker Smale model with the thermal effect. In these circumstances, we
provide analytical results for the comparison between two resulting models and
also present several numerical simulations to complement analytical results.
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