  Context. Gamma-ray binaries are systems that radiate the dominant part of
their non-thermal emission in the gamma-ray band. In a wind-driven scenario,
these binaries are thought to consist of a pulsar orbiting a massive star,
accelerating particles in the shock arising in the wind collision. Aims. We
develop a comprehensive, numerical model for the non-thermal emission of shock
accelerated particles including the dynamical effects of fluid instabilities
and orbital motion. We demonstrate the model on a generic binary system.
Methods. The model is built on a dedicated three-dimensional particle transport
simulation for the accelerated particles dynamically coupled to a simultaneous
relativistic hydrodynamic simulation of the wind interaction. In a
post-processing step, a leptonic emission model involving synchrotron and
inverse Compton emission is evaluated based on resulting particle distributions
and fluid solutions, consistently accounting for relativistic boosting and
$\gamma\gamma$-absorption in the stellar radiation field. The model is
implemented as an extension to the Cronos code. Results. In the generic binary,
the wind interaction leads to the formation of an extended, asymmetric
wind-collision region distorted by the effects of orbital motion, mixing and
turbulence giving rise to strong shocks terminating the pulsar wind and
secondary shocks in the turbulent fluid flow. With the presented approach it
is, for the first time, possible to consistently account for the dynamical
shock structure in particle transport processes, yielding a complex
distribution of accelerated particles. The predicted emission extends over a
broad region of energy, with significant orbital modulation in all bands.
