In this talk I review some of the different asymptotics for the relaxation-time operator, proposed in the literature, from the numerical simulation point of view. By solving the kinetic equation in some model device, a n+-n-n+ diode, we study whether these different asymptotics take place in the channel and we compare the solution to the simulation of their corresponding macroscopic equation/s for each regime. Also, we show comparisons of relaxation-time kinetic system versus full Boltzmann-Poisson system solved by DSMC. We will discuss numerically the validity of this approximation.
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