A 1D pipe finite element with rigid and deformable walls

The authors have formulated a simple 1D finite element for fluid flow and heat or mass transport by diffusion. The element is computationally efficient and suitable for modeling large systems of pipe segments. Motivation for this development came from a need for efficient computational models for mass transport within biological systems, such as blood vessel network, or capillary network within tumors. A detailed derivation of the fundamental equations is presented, with numerical examples which illustrate the element accuracy.