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

Astillero, A¹ and Santos, A.¹

¹ Departamento de Tecnologia de Computadores y Comunicaciones, Universidad de Extremadura, Spain

The uniform longitudinal flow [1] (ULF) is characterized  by a linear longitudinal velocity field u_x (x, t) = a(t)x, where a(t)=a₀/(1+a₀t), 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*).

References

[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