Simulations of viscous and compressible gas–gas flows using high-order finite difference schemes

Capuano, Marion; Bogey, Christophe; Spelt, Peter D. M.

doi:10.1016/j.jcp.2018.01.047

Cited by 17 publications

(10 citation statements)

References 55 publications

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“…In this section, we consider the interaction of a shock (Mach number 1.22) and a cylindrical helium bubble [46,47]. The computational domain is of size 22.25 cm × 8.90 cm.…”

Section: The Shock Wave Passage Through a Helium Bubblementioning

confidence: 99%

Mathematical modelling of transport phenomena in compressible multicomponent flows

Zhang¹,

Wang²

2022

Preprint

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The present article proposes a diffuse interface model for compressible multicomponent flows with transport phenomena of mass, momentum and energy (i.e., mass diffusion, viscous dissipation and heat conduction). The model is reduced from the seven-equation Baer-Nuziato type model with asymptotic analysis in the limit of instantaneous mechanical relaxations. The main difference between the present model and the Kapila's five-equation model consists in that different time scales for pressure and velocity relaxations are assumed, the former being much smaller than the latter. Thanks to this assumption, the velocity disequilibrium is retained to model the mass diffusion process. Aided by the diffusion laws, the final model still formally consists of five equations. The proposed model satisfy two desirable properties : (1) it respects the laws of thermodynamics, (2) it is free of the spurious oscillation problem in the vicinity of the diffused interface zone. For solution of the model governing equations, we implement the fractional step method to split the model into five physical steps: the hydrodynamic step, the viscous step, the heat transfer step, the heat conduction step and the mass diffusion step. The split governing equations for the hydrodynamic step formally coincide with the Kapila's five equation model and are solved with the Godunov finite volume method. The mass diffusion, viscous dissipation and heat conduction processes contribute parabolic partial differential equations that are solved with the Chebyshev method of local iterations. Numerical results show that the proposed model maintains pressure, velocity and temperature equilibrium near the diffused interface. Convergence tests demonstrate that the numerical methods achieve second order in space and time. The proposed model and numerical methods are applied to simulate the laser-driven RM instability problem in inertial confinement fusion, good agreement with experimental results are observed.

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“…In this section, we consider the interaction of a shock (Mach number 1.22) and a cylindrical helium bubble [46,47]. The computational domain is of size 22.25 cm × 8.90 cm.…”

Section: The Shock Wave Passage Through a Helium Bubblementioning

confidence: 99%

Mathematical modelling of transport phenomena in compressible multicomponent flows

Zhang¹,

Wang²

2022

Preprint

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“…This section examines advection of a circular air bubble in water. A one-dimensional version of this test case has been extensively studied before, and has been previously used as a test of robustness of the method using various diffuse-interface methods in Saurel and Abgrall (1999), Allaire et al (2002), Murrone and Guillard (2005), Johnsen and Ham (2012), Saurel et al (2009), Johnsen and Colonius (2006), Coralic and Colonius (2014), Beig and Johnsen (2015), Capuano et al (2018), and using a THINC method in Shyue and Xiao (2014). A two-dimensional advection of a bubble/drop has also been studied using a weighted-essentially non-oscillatory (WENO) and targeted-essentially non-oscillatory (TENO) schemes in Haimovich and Frankel (2017).…”

Section: Advection Of An Air Bubble In Watermentioning

confidence: 99%

Assessment of diffuse-interface methods for compressible multiphase fluid flows and elastic-plastic deformation in solids

Jain¹,

Adler²,

West³

et al. 2021

Preprint

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This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook (2007), Lele (2019), in which artificial diffusion terms are added to the individual phase mass fraction transport equations and are coupled with the other conservation equations. The second method is the gradient-form approach that is based on the quasi-conservative method of Shukla et al. (2010), in which the diffusion and sharpening terms (together called regularization terms) are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations (Tiwari et al., 2013). The third approach is the divergence-form approach that is based on the fully conservative method of Jain et al. ( 2020), in which the regularization terms are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. In the present study, all three diffuse-interface methods are used in conjunction with a fourequation, multicomponent mixture model, in which pressure and temperature equilibria are assumed among the various phases.The primary objective of this work is to compare these three methods in terms of their ability to: maintain constant interface thickness throughout the simulation; conserve mass, momentum, and energy; and maintain accurate interface shape for long-time integration. The second objective of this work is to consistently extend these methods to model interfaces between solid materials with strength. To assess and compare the methods, they are used to simulate a wide variety of problems, including (1) advection of an air bubble in water, (2) shock interaction with a helium bubble in air, (3) shock interaction and the collapse of an air bubble in water, and (4) Richtmyer-Meshkov instability of a copper-aluminum interface. The current work focuses on comparing these methods in the limit of relatively coarse grid resolution, which illustrates the true performance of these methods. This is because it is rarely practical to use hundreds of grid points to resolve a single bubble or drop in large-scale simulations of engineering interest.

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“…Here, as in [6], we use Pr = 0.7. The thermal conductivity of helium is calculated with the following polynomial fitting of experimental data [6]:…”

Section: Shock Passage Through a Cylindrical Bubblementioning

confidence: 99%

A reduced model for compressible viscous heat-conducting multicomponent flows

Zhang¹,

Wang²,

Shen³

et al. 2021

Preprint

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In the present paper we propose a reduced temperature non-equilibrium model for simulating multicomponent flows with inter-phase heat transfer, diffusion processes (including the viscosity and the heat conduction) and external energy sources. We derive three equivalent formulations for the proposed model. The first formulation consists of balance equations for partial densities, the mixture momentum, the mixture total energy, and phase volume fractions. The second formulation is symmetric and obtained by replacing the equations for the mixture total energy and volume fractions in the first formulation with balance equations for the phase total energy. Replacing one of the phase total energy equation of the second formulation with the mixture total energy equation gives the third formulation. All the three formulations assume velocity and pressure equilibrium across the material interface. These equivalent forms provide different physical perspectives and numerical conveniences. Temperature equilibration and continuity across the material interfaces are achieved with the instantaneous thermal relaxation. Temperature equilibrium is maintained during the heat conduction process. The proposed models are proved to respect the thermodynamical laws. For numerical solution, the model is split into a hyperbolic partial differential equation (PDE) system and parabolic PDE systems. The former is solved with the high-order Godunov finite volume method that ensures the pressure-velocitytemperature (PVT) equilibrium conduction. The parabolic PDEs are solved with both the implicit and the explicit locally iterative method (LIM) based on Chebyshev parameters. Numerical results are presented for several multicomponent flow problems with diffusion processes. Furthermore, we apply the proposed model to simulate the target ablation problem that is of significance to inertial confinement fusion. Comparisons with one-temperature models in literature demonstrate the ability to maintain the PVT property and superior convergence performance of the proposed model in solving multicomponent problems with diffusions.

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Simulations of viscous and compressible gas–gas flows using high-order finite difference schemes

Cited by 17 publications

References 55 publications

Mathematical modelling of transport phenomena in compressible multicomponent flows

Mathematical modelling of transport phenomena in compressible multicomponent flows

Assessment of diffuse-interface methods for compressible multiphase fluid flows and elastic-plastic deformation in solids

A reduced model for compressible viscous heat-conducting multicomponent flows

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