We start from the two-dimensional Gross-Pitaevskii equation (GPE) and develop algorithms for the ab-initio determination of the temperature (T) dependence of the mutual-friction coefficients, α and α′, and the normal-fluid density ρn, which appear as parameters in the Hall-Vinen-Bekharevich-Khalatnikov (HVBK) two-fluid model for a superfluid. In the second part of our study, we elucidate the statistical properties of two-dimensional, homogeneous, isotropic superfluid turbulence in the simplified HVBK model, with values for the mutual-friction coefficients that are comparable to those we obtain from the first part of our study. © TU Delft.