Using detailed 3D hydrodynamic simulations we study the nature of the Galactic supernova remnant (SNR) CTB 109 (G109.1-1.0), which is well-known for its semicircular shape and a bright diffuse X-ray emission feature inside the SNR. Our model has been designed to explain the observed morphology, with a special emphasis on the bright emission feature inside the SNR. Moreover, we determine the age of the remnant and compare our findings with X-ray observations. With CTB 109 we test a new method of detailed numerical simulations of diffuse young objects, using realistic initial conditions derived directly from observations. We performed numerical 3D simulations with the RAMSES code. The initial density structure has been directly taken from $^{12}$CO emission data, adding an additional dense cloud, which, when it is shocked, causes the bright emission feature. From parameter studies we obtained the position $(\ell , b)=(109.1545^∘ , -1.0078^∘)$ for an elliptical cloud with $n_\text{cloud}=25~\text{cm}^{-3}$ based on the preshock density from Chandra data and a maximum diameter of 4.54 pc, whose encounter with the supernova (SN) shock wave generates the bright X-ray emission inside the SNR. The calculated age of the remnant is about 11,000 yr according to our simulations. In addition, we can also determine the most probable site of the SN explosion. Hydrodynamic simulations can reproduce the morphology and the observed size of the SNR CTB 109 remarkably well. Moreover, the simulations show that it is very plausible that the bright X-ray emission inside the SNR is the result of an elliptical dense cloud shocked by the SN explosion wave. We show that numerical simulations using observational data for an initial model can produce meaningful results. ; Comment: 9 pages, 6 figures, accepted for publication in A&A