We analyse a model of the fluid flow between elastic walls simulating arteries actively interacting with the blood. Lubrication theory for the flow is coupled with the pressure and shear stress from the walls. The resulting nonlinear partial differential equation describes the displacement of the walls as a function of the distance along the flow and time. The equation is solved numerically using the one-dimensional integrated radial basis function network method. A solution in the form of a self-sustained train of pulses is obtained. Numerical experiments demonstrate the process of formation of the train from randomly chosen initial conditions. Dependence of the pulses on the boundary conditions is explored.
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.
We present numerical solutions of the semi-phenomenological model of self-propagating fluid pulses (auto-pulses) in the channel branching into two thinner channels, which simulates branching of a hypothetical artificial artery. The model is based on the lubrication theory coupled with elasticity and has the form of a single nonlinear partial differential equation with respect to the displacement of the elastic wall as a function of the distance along the channel and time. The equation is solved numerically using the 1D integrated radial basis function network method. Using homogeneous boundary conditions on the edges of space domain and continuity condition at the branching point, we obtained and analyzed solutions in the form of auto-pulses penetrating through the branching point from the thick channel into the thin channels. We evaluated magnitudes of the phenomenological coefficients responsible for the active motion of the walls in the model.
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