The SOLEDGE-EIRENE edge plasma code provides solutions for particle and energy transport in the plasma edge within complex and realistic 2D geometries (Bufferand et al 2015 Nucl. Fusion 55 053025). In this work, divertor detachment is simulated on HL-2M alternative magnetic configurations in pure deuterium plasma. Starting from a typical HL-2M low single-null configuration, the snowflake plus (SF+) and snowflake minus (SF-) configurations have then been investigated. Detachment of the outer target is studied in these configurations during plasma density ramps controlled by a fueling source, with constant input power and constant radial transport coefficients. Some typical characteristics of detachment, like threshold, depth and upstream window of detachment are investigated. In the three geometries, detachment onset and evolution with upstream plasma density is characterized by the gradual displacement of a radiation front from the outer target to the main X-point, as observed in experiments. It is found that, whatever the detachment in terms of particle, momentum or power dissipation, the detachment threshold is dominated primarily by the geometrical structure of the divertor plate and does not exhibit dependence on the magnetic configuration of the diverted plasma volume. In particular, the parallel connection length in the divertor is not found to affect the detachment threshold, in contrast with simple expectations from the two-point model, but in agreement with experimental findings.