  We present a flexible discretization technique for computational models of
thin tubular networks embedded in a bulk domain, for example a porous medium.
These systems occur in the simulation of fluid flow in vascularized biological
tissue, root water and nutrient uptake in soil, hydrological or petroleum wells
in rock formations, or heat transport in micro-cooling devices. The key
processes, such as heat and mass transfer, are usually dominated by the
exchange between the network system and the embedding domain. By explicitly
resolving the interface between these domains with the computational mesh, we
can accurately describe these processes. The network is efficiently described
by a network of line segments. Coupling terms are evaluated by projection of
the interface variables. The new method is naturally applicable for nonlinear
and time-dependent problems and can therefore be used as a reference method in
the development of novel implicit interface 1D-3D methods and in the design of
verification benchmarks for embedded tubular network methods. Implicit
interface, not resolving the bulk-network interface explicitly have proven to
be very efficient but have only been mathematically analyzed for linear
elliptic problems so far. Using two application scenarios, fluid perfusion of
vascularized tissue and root water uptake from soil, we investigate the effect
of some common modeling assumptions of implicit interface methods numerically.
