The nano-era of the semiconductor devices involves structures and phenomena requiring a multi-dimensional quantum description capable of taking into account both, purely coherent processes, such as quantization and tunneling as well as phase breaking processes of interactions with the lattice. The aim of Project P21685 'Wigner-Boltzmann Particle Simulations' is threefold: (i) Upgrade of the in-home VMC simulator to a weighted ensemble Monte Carlo code suitable for advanced classical and quantum simulations. (ii) Development of a two-dimensional particle quantum simulator based on the WIgner ENSemble (WIENS) union. (iii) Further development of WIENS as a union of theoretical and numerical approaches and algorithms for particle simulation of quantum phenomena in nanostructures. The evolution principle is the common linking element of these activities. The VMC material modules related to band structures and scattering models will be adopted directly by the ensemble counterpart. The quantum simulator is built as an extension of the two dimensional ensemble routine re-utilizing the models for boundary conditions, particle evolution, and estimators for physical averages. The algorithms and parameter settings of WIENS are used consistently with the particle generation-annihilation scheme to construct the Wigner part of the code. The classical and Wigner simulators are applied for simulation of actual devices where Boltzmann or quantum-dissipative conditions of transport dominate the device behavior. The work on WIENS continues to address open physical and numerical issues related to the Wigner picture of statistical mechanics, which are resolved by theoretical analysis and numerical experiments. A new approach, suitable for the cases where the transport is close to coherent or is determined by processes of dissipation, is suggested. Under the assumption that the Wigner function in the considered limiting case is known, we theoretically and numerically investigate the equation for the corresponding correction. The approach involves an interface with other numerical methods that are efficient in providing the limiting solution.