Flux globalization based well-balanced central-upwind scheme for one-dimensional blood flow models

Chu, Shaoshuai; Kurganov, Alexander

doi:10.1007/s10092-022-00497-y

Cited by 2 publications

(3 citation statements)

References 21 publications

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“…(ii) It preserves the discrete version of the man-at-eternal-rest (12); this means that, given the initial data:…”

Section: Theoretical Results and Numerical Experimentsmentioning

confidence: 99%

“…Most of these references address the study of the well-balanced property using the hydrostatic reconstruction technique. More recently, a new and robust second-order well-balanced central-upwind scheme for (1D) blood flow models was developed in [12]. In this work, not only the well-balanced property was addressed, but also it was rigorously shown that the proposed scheme was entropy-stable.…”

Section: Introductionmentioning

confidence: 99%

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A Steady-State-Preserving Numerical Scheme for One-Dimensional Blood Flow Model

Vega,

Valbuena,

Bojato

2024

Mathematics

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In this work, an entropy-stable and well-balanced numerical scheme for a one-dimensional blood flow model is presented. Such a scheme was obtained from an explicit entropy-conservative flux along with a second-order discretisation of the source term by using centred finite differences. We prove that the scheme is entropy-stable and preserves steady-state solutions. In addition, some numerical examples are included to test the performance of the proposed scheme.

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“…(ii) It preserves the discrete version of the man-at-eternal-rest (12); this means that, given the initial data:…”

Section: Theoretical Results and Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Steady-State-Preserving Numerical Scheme for One-Dimensional Blood Flow Model

Vega,

Valbuena,

Bojato

2024

Mathematics

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“…It provides an opportunity to obtain a robust Riemann solution for blood flow model both numerically and analytically. The reader might refer to previous studies [11][12][13][14][15][16] for further information on these Riemann solutions.…”

Section: Introductionmentioning

confidence: 99%

On the Riemann problem and interaction of elementary waves for two‐layered blood flow model through arteries

Jana,

Kuila

2023

Math Methods in App Sciences

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In this paper, we focus on the Riemann problem for two‐layered blood flow model, which is represented by a system of quasi‐linear hyperbolic partial differential equations (PDEs) derived from the Euler equations by vertical averaging across each layer. We consider the Riemann problem with varying velocities and equal constant density through arteries. For instance, the flow layer close to the wall of vessel has a slower average speed than the layer far from the vessel because of the viscous effect of the blood vessel. We first establish the existence and uniqueness of the corresponding Riemann solution by a thorough investigation of the properties of elementary waves, namely, shock wave, rarefaction wave, and contact discontinuity wave. Further, we extensively analyze the elementary wave interaction between rarefaction wave and shock wave with contact discontinuity and rarefaction wave and shock wave. The global structure of the Riemann solutions after each wave interaction is explicitly constructed and graphically illustrated towards the end.

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Flux globalization based well-balanced central-upwind scheme for one-dimensional blood flow models

Cited by 2 publications

References 21 publications

A Steady-State-Preserving Numerical Scheme for One-Dimensional Blood Flow Model

A Steady-State-Preserving Numerical Scheme for One-Dimensional Blood Flow Model

On the Riemann problem and interaction of elementary waves for two‐layered blood flow model through arteries

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