Building energy simulation is playing a key role in building design in order to reduce the energy consumption and, consequently, the CO2 emissions. An object-oriented tool called NEST is used to simulate all the phenomena that appear in a building. In the case of energy and momentum conservation and species transport, the current solver behaves well, but in the case of mass conservation it takes a lot of time to reach a solution. For this reason, in this work, instead of solving the continuity equations explicitly, an implicit method based on the Trust Region algorithm is proposed. Previously, a study of the properties of the model used by NEST-Building software has been done in order to simplify the requirements of the solver. For a building with only 9 rooms the new solver is a thousand times faster than the current method.