**Analysis of the longitudinal
uniform flow in a granular gas by means of computer grid DSMC simulations**

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__Astillero,
A__^{1} and Santos, A.^{1}

^{1} Departamento de Tecnologia de
Computadores y Comunicaciones, Universidad de Extremadura, Spain

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The uniform longitudinal flow [1]
(ULF) is characterized by a linear longitudinal velocity field u_{x}
(x, t) = a(t)x, where a(t)=a_{0}/(1+a_{0}t), a uniform density
n(t)µ a(t), and a uniform
temperature T(t). In a granular gas characterized by a given value of the
coefficient of normal restitution $\alpha$, the relevant control parameter of
the problem is the reduced deformation rate a* = a(t) / n(t) (which plays the role of the
Knudsen number), where n(t) µ n(t) _{} is an effective
collision frequency. The relevant response parameter is a nonlinear viscosity
function h*(a*) defined from the
difference between the normal stress P_{xx}(t) and the hydrostatic
pressure p(t)=n(t)T(t).

In this work, we consider a single granular gas under conditions of uniform longitudinal flow and analyze the temporal evolution of the gas in the hydrodynamic stage. We compare the results for the nonlinear viscosity function h*(a*) obtained by means of a BGK-like kinetic model and by DSMC computer grid simulations. The results show a good agreement both for the steady-state point and for the whole non-Newtonian function h*(a*).

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**References**

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[1] A. Santos, in Rarefied Gas Dynamics: Proceedings of the 26th International Symposium on Rarefied Gas Dynamics, Takashi Abe, ed. (AIP Conference Proceedings, vol. 1084, Melville, NY, 2009), pp. 93-98