Effective model of the fluid flow through elastic tube with variable radius

We study the flow of an incompressible viscous Newtonian fluid through a tube with compliant walls. The tube is assumed to be straight, long, with circular cross–sections of variable radius. Elastic properties of the tube wall are described by the linear membrane shell equations. The flow is driven by the pulsatile inlet and outlet dynamic pressure data. Applying asymptotic techniques we derive a closed reduced model. The model is of mixed hyperbolic–parabolic type with memory effects. This two dimensional model can be solved as a system of two one–dimensional problems, so it has the complexity of one-dimensional problems. This provides an efficient numerical algorithm for a model that captures leading order 2–dimensional effects.