A unified variational approach for coupling 3D–1D models and its blood flow applications

In this work, we propose an extended variational formulation in order to handle the problem of the flow of an incompressible fluid in compliant vessels with discontinuous fields. This approach makes possible to tackle in a consistent variational manner problems like the coupling between models of different dimensionality. The main ideas of the work are presented for a simple heat transfer problem and then are used in the context of modelling blood flow in large vessels. A computational implementation of the proposed formulation is also shown and discussed by presenting examples of practical applications.