A shallow water with variable pressure model for blood flow simulation
TLDR
In this paper, numerical simulations of blood flow in arteries with a variable stiffness and cross-section at rest using a finite volume method coupled with a hydrostatic reconstruction of the variables at the interface of each mesh cell were performed.Abstract:
We performed numerical simulations of blood flow in arteries with a variable stiffness and cross-section at rest using a finite volume method coupled with a hydrostatic reconstruction of the variables at the interface of each mesh cell. The method was then validated on examples taken from the literature. Asymptotic solutions were computed to highlight the effect of the viscous and viscoelastic source terms. Finally, the blood flow was computed in an artery where the cross-section at rest and the stiffness were varying. In each test case, the hydrostatic reconstruction showed good results where other simpler schemes did not, generating spurious oscillations and
nonphysical velocities.read more
Citations
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Journal ArticleDOI
A 2D nonlinear multiring model for blood flow in large elastic arteries
TL;DR: It is shown that the finite volume numerical solution of the multiring model provides at a reasonable computational cost an asymptotically valid description of blood flow velocity profiles and other averaged quantities in large elastic and quasi-rigid arteries.
Journal ArticleDOI
Low-Shapiro hydrostatic reconstruction technique for blood flow simulation in large arteries with varying geometrical and mechanical properties
TL;DR: The results indicate that HR is not adapted to compute blood flow in large arteries as it is unable to capture wave reflections and transmissions when large variations of the arteries' geometrical and mechanical properties are considered, and HR-S is exactly well-balanced and is the most accurate hydrostatic reconstruction technique.
Journal ArticleDOI
Mathematics and Numerics for Balance Partial Differential-Algebraic Equations (PDAEs)
Wanderson Lambert,Amaury Alvarez,Ismael Ledoino,Duilio Tadeu,Dan Marchesin,Johannes Bruining +5 more
TL;DR: An alternative formulation to study numerically and theoretically the PDAEs is proposed by changing the algebraic conditions into partial differential equations with relaxation source terms (PDREs), which is naturally parallelizable and has faster convergence.
Dissertation
Reduced-order models for blood flow in networks of large arteries
TL;DR: This work has focused on one-dimensional models for blood flow and developed novel approaches that take into account the non-Newtonian behavior of blood and the viscoelastic response of the arterial wall, and proposed a fluid-structure interaction twodimensional blood flow model to capture the complex flow patterns in stenoses and aneurysms unavailable to classical one- dimensional models.
Book ChapterDOI
Reduced-Order Models for Blood Pressure Drop Across Arterial Stenoses
TL;DR: In this article, the authors used four different blood flow models to compute the pressure in an idealized geometry of stenosis: the steady RNSP model, the Multi-Ring model, 1D model, and algebraic models.
References
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Book
Finite Volume Methods for Hyperbolic Problems
TL;DR: The CLAWPACK software as discussed by the authors is a popular tool for solving high-resolution hyperbolic problems with conservation laws and conservation laws of nonlinear scalar scalar conservation laws.
Book
Numerical methods for conservation laws
TL;DR: In this paper, the authors describe the derivation of conservation laws and apply them to linear systems, including the linear advection equation, the Euler equation, and the Riemann problem.
Journal ArticleDOI
On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws
TL;DR: This paper reviews some of the recent developments in upstream difference schemes through a unified representation, in order to enable comparison between the various schemes.
Waves in fluids
TL;DR: One-dimensional waves in fluids as discussed by the authors were used to describe sound waves and water waves in the literature, as well as the internal wave and the water wave in fluids, and they can be classified into three classes: sound wave, water wave, and internal wave.
Book
Numerical Approximation of Hyperbolic Systems of Conservation Laws
TL;DR: In this paper, the authors define and define nonlinear hyperbolic systems in one space dimension and define finite difference schemes for one-dimensional systems in the case of multidimensional systems.