Unsteady flow in a 2D elastic tube with the LBGK method

We report results of unsteady, harmonic flow simulations with the lattice BGK method in two-dimensional elastic tubes. The tubes are assumed to obey a simple constitutive equation, linearly relating the diameter of the tube to the pressure difference inside and outside the tube. First, as a benchmark, we present results of steady flow in such elastic tubes, and compare the performance of three different boundary conditions for the solid wall. Next, we present results of unsteady (harmonic) flow in the elastic tube, and validate the results by comparing them with theoretical expressions for the dispersion relation of the complex speed of traveling waves in the tube. Within the range of Womersley numbers tested the agreement between the simulations and the theory is good.