Projection-based resolved interface 1D-3D mixed-dimension method for embedded tubular network systems

We present a novel numerical 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 often 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 models, 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.