This paper presents a numerical investigation of the solution of the steady-state one-dimensional Drift Flux Model. It is proposed that these simulations, though often based on finite-volume discretizations and iterative sequential procedures, are preferably performed using established numerical methods specifically devised for Differential-Algebraic Equations (DAE) systems. Both strategies were implemented in a computer code developed for simulations of multicomponent hydrocarbon two-phase flows. The SIMPLER semi-implicit algorithm was employed in the solution of the finite-volume discretized model in order to provide comparison grounds with the adaptive BDF-implementation of DAE integration package DASSLC. Based on test simulations of a naphtha two-phase flow under varying heat-transfer conditions, the DAE approach was proved highly advantageous in terms of computational requirements and accuracy of results, both in the absence and presence of flow-pattern transitions. Numerical difficulties arising from the latter were successfully worked around by continuously switching regime-specific constitutive, correlations using adjustable steep regularization functions. (C) 2017 Elsevier Ltd. All rights reserved.