Reconstruction of the pressure in the method of asymptotic partial decomposition for the flows in tube structures

The method of asymptotic partial decomposition of a domain (MAPDD) proposed and justified earlier for thin domains (rod structures, tube structures consisting of a set of thin cylinders) generates some special interface conditions between the three-dimensional and one-dimensional parts. In the case of fluid mechanics this method generates a variational formulation of the velocity with Poiseuille type or Womersley type flow in the tubes at a small distance from the ends. However, the pressure should then be reconstructed using the obtained velocity field. In the present paper the procedure of the reconstruction of pressure is given and justified by the estimates between the exact pressure of the full geometry problem and the reconstructed one.