A fully well-balanced scheme for the 1D blood flow equations with friction source term

Ghitti, Beatrice; Berthon, Christophe; Le, Minh Hoang; Toro, Eleuterio F.

doi:10.1016/j.jcp.2020.109750

Cited by 25 publications

(18 citation statements)

References 21 publications

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“…All along its construction, we will carefully choose the used relations for this purpose. We adapt to the RSW system the strategy proposed in [28,29,16] for different systems.…”

Section: Approximate Riemann Solvermentioning

confidence: 99%

“…Nothing ensures these intermediate fluid heights to be positive. To address this issue, we adapt the cut-off procedure suggested in [2,28,16]. Let us introduce the threshold…”

Section: This Leads To Two Intermediate States W ⋆mentioning

confidence: 99%

“…The first fully well-balanced and positive preserving scheme was derived by Berthon-Chalons [6]. Later, fully well-balanced schemes were also derived for the shallow-water equations with both topography and friction in [29] and for the blood flow equations in [16].…”

Section: Introductionmentioning

confidence: 99%

“…For other systems with source terms, well-balanced second-order extensions exist. The reader is referred for instance to [8,28] for the shallow-water system with topography, [29] for the shallowwater system with both topography and friction and [16] for the blood flow equations. In all these extensions, the main ingredient lies in a reconstruction procedure that preserves the discrete steady states.…”

Section: Introductionmentioning

confidence: 99%

“…In [29] and [16], a discrete steady state detection procedure is performed. The purpose is to modify the limitation procedure in order to recover the well-balanced first-order scheme near steady states and keep the high-order scheme far from steady state.…”

Section: Introductionmentioning

confidence: 99%

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A fully well-balanced scheme for shallow water equations with Coriolis force

Desveaux¹,

Masset²

2021

Preprint

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The present work is devoted to the derivation of a fully well-balanced and positivepreserving numerical scheme for the shallow water equations with Coriolis force. The first main issue consists in preserving all the steady states, including the geostrophic equilibrium. Our strategy relies on a Godunov-type scheme with suitable source term and steady state discretisations. The second challenge lies in improving the order of the scheme while preserving the fully well-balanced property. A modification of the classical methods is required since no conservative reconstruction can preserve all the steady states in the case of rotating shallow water equations. A steady state detector is used to overcome this matter. Some numerical experiments are presented to show the relevance and the accuracy of both first-order and second-order schemes.

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“…All along its construction, we will carefully choose the used relations for this purpose. We adapt to the RSW system the strategy proposed in [28,29,16] for different systems.…”

Section: Approximate Riemann Solvermentioning

confidence: 99%

“…Nothing ensures these intermediate fluid heights to be positive. To address this issue, we adapt the cut-off procedure suggested in [2,28,16]. Let us introduce the threshold…”

Section: This Leads To Two Intermediate States W ⋆mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A fully well-balanced scheme for shallow water equations with Coriolis force

Desveaux¹,

Masset²

2021

Preprint

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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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Sources and Multidimensions

Toro

2024

Computational Algorithms for Shallow Water Equations

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A fully well-balanced scheme for the 1D blood flow equations with friction source term

Cited by 25 publications

References 21 publications

A fully well-balanced scheme for shallow water equations with Coriolis force

A fully well-balanced scheme for shallow water equations with Coriolis force

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

Sources and Multidimensions

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