Simulation of shock-induced bubble collapse using a four-equation model

Goncalves, Éric; Hoarau, Yannick; Zeidan, Dia

doi:10.1007/s00193-018-0809-1

Cited by 34 publications

(20 citation statements)

References 34 publications

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“…15 and 16. In fact, similar observations with respect to the mesh dependency for the same shock-bubble interaction were recently reported by Shukla (2014) and Goncalves et al (2019) using density-based methods. The mesh with 200 cells per initial bubble diameterd 0 , on the other hand, yields significantly different results compared to the meshes with higher resolution, which affects the position of the shock wave as well as the shape of the bubble, as evident by comparing Fig.…”

Section: Two-dimensional Air-bubble In Watersupporting

confidence: 86%

Numerical modelling of shock-bubble interactions using a pressure-based algorithm without Riemann solvers

Denner

Wachem

2019

Exp. Comput. Multiph. Flow

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The interaction of a shock wave with a bubble features in many engineering and emerging technological applications, and has been used widely to test new numerical methods for compressible interfacial flows. Recently, density-based algorithms with pressure-correction methods as well as fully-coupled pressure-based algorithms have been established as promising alternatives to classical density-based algorithms based on Riemann solvers. The current paper investigates the predictive accuracy of fully-coupled pressure-based algorithms without Riemann solvers in modelling the interaction of shock waves with one-dimensional and two-dimensional bubbles in gas-gas and liquid-gas flows. For a gas bubble suspended in another gas, the mesh resolution and the applied advection schemes are found to only have a minor influence on the bubble shape and position, as well as the behaviour of the dominant shock waves and rarefaction fans. For a gas bubble suspended in a liquid, however, the mesh resolution has a critical influence on the shape, the position and the post-shock evolution of the bubble, as well as the pressure and temperature distribution.

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Section: Two-dimensional Air-bubble In Watersupporting

confidence: 86%

Numerical modelling of shock-bubble interactions using a pressure-based algorithm without Riemann solvers

Denner

Wachem

2019

Exp. Comput. Multiph. Flow

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“…Whenever we use a numerical technique to solve a differential equation, we would like to make sure that the numerical solution obtained is a sufficiently good approximation to the actuality solution, some necessary definition and remarks are introduced to discuss the stability analysis [ 27 , 49 – 54 ].…”

Section: Preliminariesmentioning

confidence: 99%

Solving Time-Space-Fractional Cauchy Problem with Constant Coefficients by Finite-Difference Method

Edwan

Saadeh

Hadid

et al. 2020

Forum for Interdisciplinary Mathematics

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In this chapter, we present the time-space-fractional Cauchy equation with constant coefficients, the space and time-fractional derivative are described in the Riemann-Liouville sense and Caputo sense, respectively. The implicit scheme is introduced to solve time-space-fractional Cauchy problem in a matrix form by utilising fractionally Grünwald formulas for discretization of Riemann-Liouville fractional integral, and L1-algorithm for the discretization of time-Caputo fractional derivative, additionally, we provided a proof of the von Neuman type stability analysis for the fractional Cauchy equation of fractional order. Several numerical examples are introduced to illustrate the behaviour of approximate solution for various values of fractional order.

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“…Zeidan et al 21 investigated the problem of two‐phase two‐fluid compressible flows using relatively modern shock‐capturing methods of a centred‐type such as the total variation diminishing slope limiter centre scheme. Goncalves et al 22 considered the interaction of a planar incident shock wave with a cylindrical gas bubble in an inviscid compressible one‐fluid and examined the effect of the strength of the incident shock. Moreover, Zeidan et al 23 investigated the model of two‐phase non‐equilibrium flows and used the Godunov methods of centered type based on their Riemann solutions.…”

Section: Introductionmentioning

confidence: 99%

Lie symmetries for analyzing interaction of a characteristic shock with a singular surface in a non‐ideal reacting gas with dust particles

Shah

Singh

2020

Math Methods in App Sciences

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Using the invariance group properties of the system describing one‐dimensional unsteady flow of a non‐ideal dusty reacting gas, the evolutions of characteristic shock and singular surface are investigated. The effects of non‐idealness, reaction mechanism, and dusty gas parameters on the characteristic shock and singular surface are analyzed. Further, the amplitude of reflected wave and (or) transmitted wave along with bounce in the acceleration of shock, which generated from the interaction of a characteristic shock with a singular surface, are obtained.

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Simulation of shock-induced bubble collapse using a four-equation model

Cited by 34 publications

References 34 publications

Numerical modelling of shock-bubble interactions using a pressure-based algorithm without Riemann solvers

Numerical modelling of shock-bubble interactions using a pressure-based algorithm without Riemann solvers

Solving Time-Space-Fractional Cauchy Problem with Constant Coefficients by Finite-Difference Method

Lie symmetries for analyzing interaction of a characteristic shock with a singular surface in a non‐ideal reacting gas with dust particles

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