Context. The interstellar bubble RCW 120 seen around a type O runaway star is driven by the stellar wind and the ionising radiation emitted by the star. The boundary between the stellar wind and interstellar medium (ISM) is associated with the arc-shaped mid-infrared dust emission around the star within the HII region. Aims. We aim to investigate the arc-shaped bow shock in RCW 120 by means of numerical simulations, including the radiation, dust, HII region, and wind bubble. Methods. We performed 3D radiation-hydrodynamic simulations including dust using the GUACHO code. Our model includes a detailed treatment of dust grains in the ISM and takes into account the drag forces between dust and gas and the effect of radiation pressure on the gas and dust. The dust is treated as a pressureless gas component. The simulation uses typical properties of RCW 120. We analyse five simulations to deduce the effect of the ionising radiation and dust on both the emission intensity and the shape of the shock. Results. The interaction of the wind and the ionising radiation from a runaway star with the ISM forms an arc-shaped bow shock where the dust from the ISM accumulates in front of the moving star. Moreover, the dust forms a second small arc-shaped structure within the rarefied region at the back of the star inside the bubble. In order to obtain the decoupling between the gas and the dust, it is necessary to include the radiation-hydrodynamic equations together with the dust and the stellar motion. In this work all these elements are considered together, and we show that the decoupling between gas and dust obtained in the simulation is in agreement with the morphology of the infrared observations of RCW 120.