  We have constructed a lattice Wigner-Weyl code that generalizes the
Buot-Jensen algorithm to the calculation of electron transport in
two-dimensional circular-cylindrically symmetric structures, where the Wigner
function equation is solved self-consistently with the Poisson equation. Almost
all of the numerical simulations to date have dealt with the restriction of the
problem to one dimensional transport. In real devices, electrons are not
confined to a single dimension and the coulombic potential is fully present and
felt in three dimensions. We show the derivation of the 2D equation in
cylindrical coordinates as well as approximations employed in the calculation
of the four-dimensional convolution integral of the Wigner function and the
potential. We work under the assumption that longitudinal transport is more
dominant than radial transport and employ parallel processing techniques. The
total transport is calculated in two steps: (1) transport the particles in the
longitudinal direction in each shell separately, then (2) each shell exchanges
particles with its nearest neighbor. Most of this work is concerned with the
former step: A 1D space and 2D momentum transport problem. Time evolution
simulations based on these method are presented for three different cases. Each
case lead to numerical results consistent with expectations. Discussions of
future improvements are discussed.
