Interface tracking method for compressible multifluids

Chertock, Alina; Karni, Smadar; Kurganov, Alexander

doi:10.1051/m2an:2008036

Cited by 32 publications

(34 citation statements)

References 43 publications

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“…Only if the CFL condition is adapted to the contact discontinuity and set equal to 1, the solution is solved exactly. Nevertheless, in order to better solve contact discontinuities in a general case, one could use a front tracking technique like the one proposed in [4,5].…”

Section: Remark 42mentioning

confidence: 99%

A HLLC scheme for Ripa model

Sánchez-Linares¹,

Luna

Díáz³

2016

Applied Mathematics and Computation

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Section: Remark 42mentioning

confidence: 99%

A HLLC scheme for Ripa model

Sánchez-Linares¹,

Luna

Díáz³

2016

Applied Mathematics and Computation

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“…are then computed using the interpolation between (ρ J−1 ,u J−1 ,p J−1 ) and (ρ gh ,u gh ,p gh ), which is, following the idea of the multi-fluid algorithms in [6] and [5], performed in the phase space. Namely, we exactly solve the Riemann problem between the above two states.…”

Section: Boundary Cell Treatment In 1-dmentioning

confidence: 99%

“…We follow the approach from [5,6] and once again use the solution of the Riemann problem between (ρ J−1 ,u J−1 ,p J−1 ) and (ρ gh ,u gh ,p gh ) to obtain U J (t + ∆t). The correction procedure is summarized in the following algorithm:…”

Section: Boundary Cell Treatment In 1-dmentioning

confidence: 99%

“…We prefer an alternative, simpler approach, in which the averages are computed over the internal cells only and the data contained in the boundary cells are not used for the computation of numerical fluxes. We treat the boundary cells similar to the way that the so-called "mixed" cells have been treated in [5]. Namely, we only approximate the point values at the edges of these cells, required in the numerical flux computations.…”

Section: Introductionmentioning

confidence: 99%

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A simple Eulerian finite-volume method for compressible fluids in domains with moving boundaries

Chertock¹,

Kurganov²

2008

Communications in Mathematical Sciences

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Abstract. We introduce a simple new Eulerian method for treatment of moving boundaries in compressible fluid computations. Our approach is based on the extension of the interface tracking method recently introduced in the context of multifluids. The fluid domain is placed in a rectangular computational domain of a fixed size, which is divided into Cartesian cells. At every discrete time level, there are three types of cells: internal, boundary, and external ones. The numerical solution is evolved in internal cells only. The numerical fluxes at the cells near the boundary are computed using the technique from [A. Chertock, S. Karni and A. Kurganov, M2AN Math. Model. Numer. Anal., to appear] combined with a solid wall ghost-cell extrapolation and an interpolation in the phase space. The proposed computational framework is general and may be used in conjunction with one's favorite finite-volume method. The robustness of the new approach is illustrated on a number of one-and two-dimensional numerical examples.

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“…Numerical and exact methods for Euler equations with a Tammann EOS have been studied and developed previously, e.g. [45,20,86,87,90] among others; however, to the best of our knowledge, the numerical algorithms developed for this work are the only ones specifically developed to model an experimental setup with fixed sharp interfaces with a big jump in the parameters. We present some description of the methods and a verification study.…”

mentioning

confidence: 99%

Computational and In Vitro Studies of Blast-Induced Blood-Brain Barrier Disruption

Razo

Morofuji

Meabon

et al. 2016

SIAM J. Sci. Comput.

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Abstract. There is growing concern that blast-exposed individuals are at risk of developing neurological disorders later in life. Therefore, it is important to understand the dynamic properties of blast forces on brain cells, including the endothelial cells that maintain the blood-brain barrier (BBB), which regulates the passage of nutrients into the brain and protects it from toxins in the blood. To better understand the effect of shock waves on the BBB we have investigated an in vitro model in which BBB endothelial cells are grown in transwell vessels and exposed in a shock tube, confirming that BBB integrity is directly related to shock wave intensity. It is difficult to directly measure the forces acting on these cells in the transwell container during the experiments, and so a computational tool has been developed and presented in this paper.Two-dimensional axisymmetric Euler equations with the Tammann equation of state were used to model the transwell materials, and a high-resolution finite volume method based on Riemann solvers and the Clawpack software was used to solve these equations in a mixed Eulerian/Lagrangian frame. Results indicated that the geometry of the transwell plays a significant role in the observed pressure time series in these experiments. We also found that pressures can fall below vapor pressure due to the interaction of reflecting and diffracting shock waves, suggesting that cavitation bubbles could be a damage mechanism. Computations that include a simulated hydrophone inserted in the transwell suggest that the instrument itself could significantly alter blast wave properties. These findings illustrate the need for further computational modeling studies aimed at understanding possible blastinduced BBB damage.

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Interface tracking method for compressible multifluids

Cited by 32 publications

References 43 publications

A HLLC scheme for Ripa model

A HLLC scheme for Ripa model

A simple Eulerian finite-volume method for compressible fluids in domains with moving boundaries

Computational and In Vitro Studies of Blast-Induced Blood-Brain Barrier Disruption

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