The need for decision support after a flooding casualty requires the development of fast and accurate progressive flooding simulation procedures. Here, a new quasi-static technique is presented, proposing a differential algebraic formulation capable to consider independently the flooding process in the internal rooms. The proposed method is efficient while simulating long flooding chains along rooms connected by similar size openings, a condition that likely occurs on large passenger ships. Moreover, the computational performances of the simulation procedure have been enhanced by adapting the time step to the progressive flooding pace. The adoption of an adaptive time step algorithm reduces significantly the calculation time. The novel procedure has been tested on the recommended benchmark cases for flooding simulations, highlighting the accuracy and flexibility of the proposed method.