  In this work, a new Monte-Carlo simulation of double parton scattering (DPS)
at parton level is presented. The simulation is based on the QCD framework
developed recently by M. Diehl, J. R. Gaunt and K. Sch\"{o}nwald. With this
framework, the dynamics of the $1\to2$ perturbative splittings is consistently
included inside the simulation, with the impact-parameter dependence taken into
account. The simulation evolves simultaneously two hard systems from a common
hard scale down to the hadronic scale. The evolution is performed using an
angular-ordered parton shower which is combined with a set of double parton
distributions that depend explicitly on the inter-parton distance. An
illustrative study is performed in the context of same-sign WW production at
the LHC, with the quark content of the proton being limited to three flavours.
In several distributions we see differences compared to DPS models in Herwig,
Pythia, and the DPS "pocket formula".
