Explosion hazards constitute a significant practical problem for industry. In response to the need for better-resolved predictions for confined explosions, and particularly with a view to advancing safety cases for offshore oil and gas rigs, an existing unstructured, adaptive mesh, finite volume Reynolds-averaged Navier-Stokes computational fluid dynamics code (originally developed to handle non-combusting turbomachinery hows) has been modified to include a one-equation, eddy break-up combustion model. Two benefits accrue from the use of unstructured, solution-adaptive meshes: first, great geometrical flexibility is possible; second, automatic mesh adaptation allows computational effort to be focused on important or interesting areas of the flow by enhancing mesh resolution only where it is required. In the work reported here, the mesh was adaptively refined to achieve flame front capture, and it is shown that this results in a 10%-33% CPU saving for two-dimensional calculations and a saving of between 57% and 70% for three-dimensional calculations. The geometry of the three-dimensional calculations was relatively simple, and it may be expected that the use of unstructured meshes for truly complex geometries will result in CPU savings sufficient to allow an order-of-magnitude increase in either complexity or resolution. (C) 1998 John Wiley & Sons, Ltd.