  We develop a unified numerical approach for modeling
semiconductor-superconductor heterostructures. Our approach takes into account
on equal footing important key ingredients: proximity-induced
superconductivity, orbital and Zeeman effect of an applied magnetic field,
spin-orbit coupling as well as the electrostatic environment. As a model
system, we consider indium arsenide (InAs) nanowires with epitaxial aluminum
(Al) shell and demonstrate qualitative agreement of the obtained results with
the existing experimental data. Finally, we characterize the topological
superconducting phase emerging in a finite magnetic field and calculate the
corresponding topological phase diagram.
