STARBENCH: the D-type expansion of an H II region

STARBENCH is a project focused on benchmarking and validating different star formation and stellar feedback codes. In this first STARBENCH paper we perform a comparison study of the D-type expansion of an H II region. The aim of this work is to understand the differences observed between the 12 participating numerical codes against the various analytical expressions examining the D-type phase of H II region expansion. To do this, we propose two well-defined tests which are tackled by 1D and 3D grid- and smoothed particle hydrodynamics-based codes. The first test examines the `early phase' D-type scenario during which the mechanical pressure driving the expansion is significantly larger than the thermal pressure of the neutral medium. The second test examines the `late phase' D-type scenario during which the system relaxes to pressure equilibrium with the external medium. Although they are mutually in excellent agreement, all 12 participating codes follow a modified expansion law that deviates significantly from the classical Spitzer solution in both scenarios. We present a semi-empirical formula combining the two different solutions appropriate to both early and late phases that agrees with high-resolution simulations to ≲ 2 per cent. This formula provides a much better benchmark solution for code validation than the Spitzer solution. The present comparison has validated the participating codes and through this project we provide a data set for calibrating the treatment of ionizing radiation hydrodynamics codes.