Exact Solution of the Riemann Problem for the One-Dimensional Blood Flow Equations with General Constant Momentum Correction Coefficient (Communications in Computational Physics, 2024)
The momentum correction coefficient in one-dimensional blood flow models is related to the prescribed velocity profile. The exact solution of the Riemannproblem for the one-dimensional blood flow equations has been previously studiedonly for a momentum correction coefficient equal to one (corresponding to a flat velocity profile, i.e. an inviscid fluid). In this paper we solve exactly the Riemann problem for the non-linear hyperbolic one-dimensional blood flow equations with a general constant momentum correction coefficient and a tube law that allows to describeboth arteries and veins with continuous or discontinuous mechanical and geometricalproperties. In the case of discontinuous properties, only the subsonic regime is considered. We propose a numerical procedure to compute the obtained exact solutionand finally we validate it numerically, by comparing exact solutions to those obtainedwith well-known, first order, numerical schemes on a carefully designed set of testproblems. A detailed knowledge about this problem will allow to determine couplingand boundary conditions arising when these models are applied on networks of vessels, ensuring full consistency with the underlying one-dimensional blood flow modelwithout resorting to linearization techniques commonly applied when the momentumcorrection coefficient is assumed to be different from one.
Keywords: Blood flow; hyperbolic systems of PDEs; exact solution of the Riemann problem; wave relations.