A new conservative numerical scheme for flow problems on unstructured grids and unbounded domains

We consider the prototype of a flow and transport problem in two dimensions. In particular, in many fluid dynamics problems the boundary conditions may be unknown, or the domain may be unbounded. Furthermore, only numerical schemes which conserve mass and are stable with respect to dominating convection are appropriate to solve these problems. Therefore, we develop a new discrete scheme to address these issues. More precisely, we couple the cell-centered finite volume method and the boundary element method and introduce suitable transmission conditions. Also (semi-) robust a posteriori estimates of residual type are developed which allow us to use an adaptive mesh refinement algorithm to treat efficiently problems which have singularities or boundary/internal layers. Several examples illustrate the effectiveness of our new adaptive coupling method.