Simulations of autonomous fluid pulses between active elastic walls using the 1D-IRBFN method

Abstract

We present numerical solutions of the semi-empirical model of self-propagating fluid pulses (auto-pulses) through the channel simulating an artificial artery. The key mechanism behind the model is the active motion of the walls in line with the earlier model of Roberts. Our model is autonomous, nonlinear and is based on the partial differential equation describing the displacement of the wall in time and along the channel. A theoretical plane configuration is adopted for the walls at rest. For solving the equation we used the One-dimensional Integrated Radial Basis Function Network (1D-IRBFN) method. We demonstrated that different initial conditions always lead to the settling of pulse trains where an individual pulse has certain speed and amplitude controlled by the governing equation. A variety of pulse solutions is obtained using homogeneous and periodic boundary conditions. The dynamics of one, two, and three pulses per period are explored. The fluid mass flux due to the pulses is calculated.

Parameters and Branching Auto-Pulses in a Fluid Channel with Active Walls

“…Therefore, in this paper we focus on simulation of pulses in branching channels. In our recent work [1] only non-branching (single) channels were considered; this is the major difference between the two studies. In addition, in the present paper we evaluate the empirical coefficients playing the key role in our model.…”

“…While Roberts considered the case of negligible viscous forces compared to inertia, which is relevant to wider channels, we will consider the case when inertia is negligible compared to viscous forces, which is relevant to narrow channels. In the previous paper of the current authors [1], a variety of pulse solutions is obtained for a single channel. In the current paper we consider branching channels and analyse the conditions under which a pulse can successfully propagate from a thick channel into a thin one through the branching point.…”