To investigate the mechanisms leading to the heat deposition onto the first wall in the Scrape-Off Layer (SOL), we perform dedicated numerical non-linear simulations of the SOL plasma dynamics of a TCV discharge using the GBS code. The simulated parallel heat flux profiles on the limiter agree qualitatively with the experimental ones obtained by means of infrared thermography, showing a double scale length. Non-ambipolar currents are found to flow to the limiter, consistently with the experiments. The contribution of the latter to the total heat flux is discussed. The results of a second simulation identical to the first one but with 40 times higher resistivity are also discussed. (C) 2016 The Authors. Published by Elsevier Ltd.