Elementary waves, Riemann invariants, new conservation laws and
numerical method for the blood flow through artery
Abstract
In this paper we consider the quasi linear hyperbolic system of two
coupled nonlinear equations that arises in blood flow through arteries.
This model has already been reflected the human circulatory system. We
first study the parametrization of elementary waves. We formulate the
Riemann invariants corresponding to the blood flow model. Furthermore we
present an interesting and important motivation of the Riemann
invariants. We represent the diagonal form corresponding to the blood
flow model, which admits the existence of global smooth solution for this
system. We introduce further application, namely a new conservation laws
for the blood flow model. Finally, we propose a simple and accurate class
of finite volume scheme for numerical simulation of blood flow in
arteries. This scheme consists of predictor and corrector steps, the
predictor step contains a parameter of control of the numerical
diffusion of the scheme, which modulate by using limiter theory and
Riemann invariant, the corrector step recovers the balance conservation
equation. The numerical results demonstrate high resolution of the
proposed finite volume scheme (Modified Rusanov) and confirm its capability
to provide accurate simulations for blood flow under flow regimes with
strong shocks.