A high-order accurate five-equations compressible multiphase approach for viscoelastic fluids and solids with relaxation and elasticity

Rodriguez, Mauro; Johnsen, Eric

doi:10.1016/j.jcp.2018.10.035

Cited by 15 publications

(9 citation statements)

References 77 publications

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“…This method has previously been implemented for the pressure-equilibrium models of Allaire [20,21,46]; here, we also utilize it for the pressure-disequilibrium model of Saurel et al [3].…”

Section: Spatial and Time Reconstructionmentioning

confidence: 99%

An assessment of multicomponent flow models and interface capturing schemes for spherical bubble dynamics

Schmidmayer

Bryngelson

Colonius

2020

Journal of Computational Physics

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Numerical simulation of bubble dynamics and cavitation is challenging; even the seemingly simple problem of a collapsing spherical bubble is difficult to compute accurately with a general, three-dimensional, compressible, multicomponent flow solver. Difficulties arise due to both the physical model and the numerical method chosen for its solution. We consider the 5-equation model of Allaire et al. [1], the 5-equation model of Kapila et al. [2], and the 6-equation model of Saurel et al. [3] as candidate approaches for spherical bubble dynamics, and both MUSCL and WENO interface-capturing methods are implemented and compared. We demonstrate the inadequacy of the traditional 5-equation model of Allaire et al. [1] for spherical bubble collapse problems and explain the corresponding advantages of the augmented model of Kapila et al. [2] for representing this phenomenon. Quantitative comparisons between the augmented 5-equation and 6-equation models for three-dimensional bubble collapse problems demonstrate the versatility of pressure-disequilibrium models. Lastly, the performance of pressure disequilibrium model for representing a three-dimensional spherical bubble collapse for different bubble interior/exterior pressure ratios is evaluated for different numerical methods. Pathologies associated with each factor and their origins are identified and discussed.

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“…This method has previously been implemented for the pressure-equilibrium models of Allaire [20,21,46]; here, we also utilize it for the pressure-disequilibrium model of Saurel et al [3].…”

Section: Spatial and Time Reconstructionmentioning

confidence: 99%

An assessment of multicomponent flow models and interface capturing schemes for spherical bubble dynamics

Schmidmayer

Bryngelson

Colonius

2020

Journal of Computational Physics

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“…• Multi-phase and multi-material flows.A conservative Allen-Cahn equation for multiphase flows is simulated in Aihara, Takaki and Takada (2019). A compressible multiphase approach for viscoelastic fluids and solids with relaxation and elasticity was pursued in Rodriguez and Johnsen (2019). The collapse of a cloud with gas bubbles in a liquid was computed in Rasthofer et al (2019).…”

Section: Applicationsmentioning

confidence: 99%

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

Shu¹

2020

Acta Numerica

133

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Essentially non-oscillatory (ENO) and weighted ENO (WENO) schemes were designed for solving hyperbolic and convection–diffusion equations with possibly discontinuous solutions or solutions with sharp gradient regions. The main idea of ENO and WENO schemes is actually an approximation procedure, aimed at achieving arbitrarily high-order accuracy in smooth regions and resolving shocks or other discontinuities sharply and in an essentially non-oscillatory fashion. Both finite volume and finite difference schemes have been designed using the ENO or WENO procedure, and these schemes are very popular in applications, most noticeably in computational fluid dynamics but also in other areas of computational physics and engineering. Since the main idea of the ENO and WENO schemes is an approximation procedure not directly related to partial differential equations (PDEs), ENO and WENO schemes also have non-PDE applications. In this paper we will survey the basic ideas behind ENO and WENO schemes, discuss their properties, and present examples of their applications to different types of PDEs as well as to non-PDE problems.

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“…Phase change at the bubble-material interface has been incorporated with the use of fully-Eulerian Multi-component Flow Code (MFC) and a high-order accurate, shock-and interface-capturing numerical solver 19,22 . Three-dimensional fluid-structure interactions and multi-scale cavitation dynamics with linear elastic bubble surroundings has also been achieved with MFC 23 .…”

Section: Introductionmentioning

confidence: 99%

Reduced-order approach for soft material inertial cavitation rheometry

Zhu¹,

Abeid²,

Estrada³

2023

Preprint

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An understanding of inertial cavitation is crucial for biological and engineering applications such as non-invasive tissue surgeries and the mitigation of potential blast injuries. However, predictive modeling of inertial cavitation in biological tissues is hindered by the difficulties of characterizing fluids and soft materials at high strain rates, and the computational cost of calibrating biologically-relevant viscoelastic models. By incorporating a reduced-order model of inertial cavitation in the inertial microcavitation rheometry (IMR) experimental technique, we present an efficient procedure to inversely characterize viscoelastic material subjected to inertial cavitation. Instead of brute-force iteration of constitutive model parameters, the present approach directly estimates the elastic and viscous moduli according to the sizedependent scaling of bubble dynamics. Through reproduction of numerical-simulated inertial cavitation kinematics and experimental characterization of benchmark materials, we demonstrate that the proposed framework can determine the complex rate-dependent properties of soft solid with a small number of numerical simulations. The availability of this procedure will broaden the applicability of IMR for localized characterization of fluids and soft biological materials at high strain rates.

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A high-order accurate five-equations compressible multiphase approach for viscoelastic fluids and solids with relaxation and elasticity

Cited by 15 publications

References 77 publications

An assessment of multicomponent flow models and interface capturing schemes for spherical bubble dynamics

An assessment of multicomponent flow models and interface capturing schemes for spherical bubble dynamics

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

Reduced-order approach for soft material inertial cavitation rheometry

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