Augmented Riemann solver for urethra flow modeling

Brandner, Marek; Egermaier, Jiří; Kopincová, Hana

doi:10.1016/j.matcom.2009.08.009

Cited by 3 publications

(8 citation statements)

References 5 publications

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“…The discrete form of the vector ∆w corresponds to the certain approximation of these eigenvectors. It can be shown (Brandner at al., 2009) …”

Section: Steady Statesmentioning

confidence: 90%

“…The approximation is chosen to be able to prove the consistency and provide the stability of the algorithm. In some special cases this scheme is conservative and we can guarantee the positive semidefiniteness, but only under the additional assumptions (see (Brandner at al., 2009)).…”

Section: Decompositions Based On Augmented Systemmentioning

confidence: 99%

“…This, in the case of urethra flow, is more complicated because of structure of the eigenvectors. Some necessary conditions for approximation of these eigenvectors are presented in (Brandner at al., 2009). …”

Section: Positive Semidefinitenessmentioning

confidence: 99%

See 2 more Smart Citations

Numerical Schemes for Hyperbolic Balance Laws - Applications to Fluid Flow Problems

Brandner¹,

Egermaier²,

Kopincová³

2012

Finite Volume Method - Powerful Means of Engineering Design

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“…The discrete form of the vector ∆w corresponds to the certain approximation of these eigenvectors. It can be shown (Brandner at al., 2009) …”

Section: Steady Statesmentioning

confidence: 90%

Section: Decompositions Based On Augmented Systemmentioning

confidence: 99%

See 1 more Smart Citation

Numerical Schemes for Hyperbolic Balance Laws - Applications to Fluid Flow Problems

Brandner¹,

Egermaier²,

Kopincová³

2012

Finite Volume Method - Powerful Means of Engineering Design

Self Cite

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“…In this case, the vector of conservative variables, the flux vector and the source terms are respectively given by [5]:…”

Section: Case Of Urethramentioning

confidence: 99%

“…The first works on the numerical study of the flow inside elastic conduits start with Stergiopulos et al [4] who developed a method of nonlinear separation of forward and backward running waves in elastic conduits. The interest for the urethra flow modeling starts with Brandner et al [5] who proposed a numerical scheme for the male urethra and ureter fluid flow simulations. The scheme is able to maintain not only some special steady states but all possible ones.…”

Section: Introductionmentioning

confidence: 99%

TV-HLL Solver for One-Dimensional Fluid Flow Inside Elastic Vessels

Kapen

Tchuen

2016

Int. J. Appl. Comput. Math

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The TV-HLL solver for the numerical solution of fluid flow inside elastic vessels is constructed in this paper. The system of partial differential equations describing the fluid flow inside collapsible tubes is presented and solved numerically by using the finite volume method. The evaluation of the numerical flux at the interfaces is performed by using the TV-HLL scheme which is derived from the previous studies presented for solving the Euler equations Tchuen, 2014, 2015). Indeed, the present scheme is obtained by following the Toro-Vázquez splitting, and using the HLL algorithm with modified wave speeds for the pressure system. An essential feature of the TV-HLL scheme is to associate two systems of differential equations, called the advection system and the pressure system. The proposed scheme preserves the non-negativity of essentially nonnegative quantities (cross section). It has been applied to some one-dimensional numerical tests dealing with the fluid flow through the male urethra and the blood flow inside cerebral vessels.

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A well-balanced solver for the Saint Venant equations with variable cross-section

Borsche¹

2015

Journal of Numerical Mathematics

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In this paper we construct a numerical solver for the Saint Venant equations. Special attention is given to the balancing of the source terms, including the bottom slope and variable cross-sectional profiles. Therefore a special discretization of the pressure law is used, in order to transfer analytical properties to the numerical method. Based on this approximation awell-balanced solver is developed, assuring the C-property and depth positivity. The performance of this method is studied in several test cases focusing on accurate capturing of steady states.

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Augmented Riemann solver for urethra flow modeling

Cited by 3 publications

References 5 publications

Numerical Schemes for Hyperbolic Balance Laws - Applications to Fluid Flow Problems

Numerical Schemes for Hyperbolic Balance Laws - Applications to Fluid Flow Problems

TV-HLL Solver for One-Dimensional Fluid Flow Inside Elastic Vessels

A well-balanced solver for the Saint Venant equations with variable cross-section

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