Study of wave propagation in arterial blood flow under symmetry analysis

In this paper, we address a one-dimensional quasi-linear hyperbolic system of equations describing blood flow through compliant axi-symmetric vessels. From the symmetry analysis, we derive symmetry group of transformations and the corresponding symmetry generators by analyzing the parameters. Next, with the help of symmetry generators and invariant functions, we construct and classify the optimal system of subalgebras. Further, we obtained the similarity variables and similarity forms for each subalgebra leading to the reduction of the given governing coupled PDEs to the system of ODEs. Moreover, we studied the nature of blood flow velocity as well as the cross-sectional area of the arteries under the influence of arterial stiffness s$$ s $$ graphically. Finally, the evolutionary behavior of weak discontinuity in the blood flow pattern is discussed with respect to aging.