We introduce version 6.0 of the 2D multispecies plasma fluid code 132, to which a flexible dynamic grid adaptation module has been added. The method followed in this paper involves the creation of two grid structures. A fine 2D mesh produced from the magnetic flux surface structure serves as a scaffolding on which a rougher, adaptable mesh is constructed depending on the physical situation. The conditions for grid refinement/coarsening involve normalized gradients of the plasma parameters. The algorithm and its numerical implementation are described in detail. As a sample application, the detachment behaviour of an ASDEX-Upgrade L- Mode discharge has been studied. A comparison of the results from the old and new B2 code versions is presented. Similar results in the overall plasma behaviour are seen but differences appear in the detachment zone, due to the grid adapting to the strong local gradients. Increased (decreased) gas puffing leads to an upward (downward) shift of the detachment front as well as to a shift of the zone of maximum grid density. The now code allows one to increase the grid density in the zone of interest without a strong increase CPU runtime, thus enabling a more realistic modelling of the detachment front