2014
DOI: 10.1002/cnm.2651
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An efficient semi‐implicit method for three‐dimensional non‐hydrostatic flows in compliant arterial vessels

Abstract: Blood flow in arterial systems can be described by the three-dimensional Navier-Stokes equations within a time-dependent spatial domain that accounts for the elasticity of the arterial walls. In this article, blood is treated as an incompressible Newtonian fluid that flows through compliant vessels of general cross section. A three-dimensional semi-implicit finite difference and finite volume model is derived so that numerical stability is obtained at a low computational cost on a staggered grid. The key idea … Show more

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Cited by 18 publications
(22 citation statements)
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“…the pressure is a nonnegative function of bounded variation. 13,14,[81][82][83][84][85] Due to the properties of T r , the linear subproblems within the Newton-type algorithm can be solved at the aid of a matrix-free conjugate gradient method or with the Thomas algorithm for tridiagonal systems in the one-dimensional case. It is therefore possible to employ the same (nested) Newton-type techniques for the solution of (23) as those proposed and analyzed by Casulli et al [37][38][39][40] For all implementation details and a rigorous convergence proof of the (nested) Newton method, the reader is referred to the above references.…”
Section: Pressure Subsystemmentioning
confidence: 99%
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“…the pressure is a nonnegative function of bounded variation. 13,14,[81][82][83][84][85] Due to the properties of T r , the linear subproblems within the Newton-type algorithm can be solved at the aid of a matrix-free conjugate gradient method or with the Thomas algorithm for tridiagonal systems in the one-dimensional case. It is therefore possible to employ the same (nested) Newton-type techniques for the solution of (23) as those proposed and analyzed by Casulli et al [37][38][39][40] For all implementation details and a rigorous convergence proof of the (nested) Newton method, the reader is referred to the above references.…”
Section: Pressure Subsystemmentioning
confidence: 99%
“…The iterative Newton-type techniques of Casulli et al have already been used with great success as building block of semi-implicit finite volume schemes in different application contexts, see other works. 13,14,[81][82][83][84][85] Due to the properties of T r , the linear subproblems within the Newton-type algorithm can be solved at the aid of a matrix-free conjugate gradient method or with the Thomas algorithm for tridiagonal systems in the one-dimensional case. Note that, for the ideal gas EOS, the resulting system (23) becomes linear in the pressure; hence, one single Newton iteration is sufficient to solve (23).…”
Section: Pressure Subsystemmentioning
confidence: 99%
“…Numerical simulations of blood flow in veins or arteries have been carried out by several authors, see e.g. [17,15,1,2,16]. In contrast our mathematical model can be solved with a simple and very efficient numerical method.…”
Section: Numerical Implementationmentioning
confidence: 99%
“…The θ -method is widely used in the semi-implicit schemes (see [8,12,14,17,30,32]) because is it quite a simple and cheap strategy to achieve second order of accuracy in time.…”
Section: Semi-implicit Finite Volume Schemesmentioning
confidence: 99%
“…To improve the information that regards the radial velocity profile, one can use a semi-implicit scheme for a twodimensional model such as the one suggested in [14]. This method is an extension to weakly compressible flows of the family of semi-implicit methods for blood flow presented in a series of recent papers [8,17,32]. Under the hypothesis of hydrostatic radial pressure equilibrium and when the longitudinal scale is much larger than the radial one, the motion of a compressible barotropic fluid in a circular elastic duct is described by the following system of equations, which is a simplification of the Navier-Stokes equation in cylindrical coordinates:…”
Section: Semi-implicit Finite Volume Schemesmentioning
confidence: 99%