A Numerical Method for Two-Phase Flow Consisting of Separate Compressible and Incompressible Regions

Caiden, Rachel; Fedkiw, Ronald; Anderson, Christopher R.

doi:10.1006/jcph.2000.6624

Cited by 130 publications

(133 citation statements)

References 34 publications

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“…The only information needed from Ω L is the velocity vector evaluated at the boundary. This conclusion is similar to the one obtained in [33] for coupling compressible to incompressible flow.…”

Section: Coupling Schemesupporting

confidence: 90%

A level set approach to Eulerian–Lagrangian coupling

Arienti

Hung

Morano

et al. 2003

Journal of Computational Physics

125

102

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Section: Coupling Schemesupporting

confidence: 90%

A level set approach to Eulerian–Lagrangian coupling

Arienti

Hung

Morano

et al. 2003

Journal of Computational Physics

125

102

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“…The basic idea is to consider two copies of the solution and, by defining ghost values that implicitly capture jump conditions, avoid numerically differentiating across discontinuities . This methodology has been applied to a wide range of applications including deflagration in Fedkiw et al [43], compressible/incompressible fluids in Caiden et al [24], flame propagation in Nguyen et al [97], the Poisson equation with jump conditions in Liu et al [78], free surface flows in Enright et al [40], as well as in computer graphics [96,39]. It was developed for the Poisson and the diffusion equations on irregular domains with Dirichlet boundary conditions and their applications in Gibou et al [47,45,44,46].…”

Section: The Ghost-fluid Methods For the Diffusion And The Poisson Equmentioning

confidence: 99%

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

2012

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We present a review of some of the state-of-the-art numerical methods for solving the Stefan problem and the Poisson and the diffusion equations on irregular domains using (i) the level-set method for representing the (possibly moving) irregular domain's boundary, (ii) the ghost-fluid method for imposing the Dirichlet boundary condition at the irregular domain's boundary and (iii) a quadtree/octree nodebased adaptive mesh refinement for capturing small length scales while significantly reducing the memory and CPU footprint. In addition, we highlight common misconceptions and describe how to properly implement these methods. Numerical experiments illustrate quantitative and qualitative results.

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“…The subscripts g and l denote gas and liquid respectively. Equations (2) and (3) give the two-phase dynamical system.…”

Section: Two-phase Flow Modelmentioning

confidence: 99%

“…Presently, the flow of interest consists of a gaseous carrier phase with many suspended water droplets. These two fluids' parameters are drastically different and the vast majority of numeric methods in the literature are ill-adapted since they introduce artificial diffusion and mixing at interfaces [1][2][3]. Other methods are poorly suited to mixtures where thermodynamic equilibrium cannot be reasonably assumed except at interfaces.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control of Shock Wave Attenuation using Liquid Water Droplets with Application to Ignition Overpressure in Launch Vehicles

Moshman¹,

Sritharan²,

Hobson³

2011

International Journal of Flow Control

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This paper presents the first solution of an optimal control problem concerning unsteady blast wave attenuation where the control takes the form of the initial distribution of liquid water droplets. An appropriate two-phase flow model is adopted for compressible homogeneous two-phase flows. The dynamical system includes an empirical model for water droplet vaporization, the dominant mechanism for attenuating the jump in pressure across the shock front. At the end of the simulation interval, an appropriate target state is defined such that the jump in pressure of the target state is less than that of the simulated blast wave. Given the nature of the non-linear system, the final time must also be a free variable. A novel control algorithm is presented which can satisfy all necessary conditions of the optimal system and avoid taking a variation at the shock front. The adjoint-based method is applied to NASA's problem of Ignition Overpressure blast waves generated during ignition of solid grain rocket segments on launch vehicles. Results are shown for a range of blast waves that are plausible to see in the launch environment of the shuttle. Significant parameters of effective droplet distributions are identified. INTRODUCTIONThere exists a wide range of multi-phase and multi-fluid flow regimes. Much care must be taken in selecting an appropriate model and numeric method. Presently, the flow of interest consists of a gaseous carrier phase with many suspended water droplets. These two fluids' parameters are drastically different and the vast majority of numeric methods in the literature are ill-adapted since they introduce artificial diffusion and mixing at interfaces [1][2][3]. Other methods are poorly suited to mixtures where thermodynamic equilibrium cannot be reasonably assumed except at interfaces. Since the water droplets of interest will be smaller than 1 mm, their properties can be assumed to be homogeneous between computational cells and, therefore, many interfaces will be present in each cell. It will be impractical to use interface tracking methods or solve separate sets of equations for each fluid and to couple their properties at the interface. Instead, the following calculations implement a method proposed by [4] which has the advantage of solving the same set of differential equations throughout the domain. The method uses different equations of state for each phase and allows a difference in temperature at the gas-liquid interfaces. To close the system, a volume fraction variable α is introduced and a non-conservative PDE is appended to the conservative system. The method assumes that both phases are compressible which yields a hyperbolic system. Ignition overpressure (IOP) is a phenomenon present at the start of an ignition sequence in launch vehicles using solid-grain propellants. When the grain is ignited the pressure inside the combustion chamber quickly rises several orders of magnitude. This drives hot combustion products toward the nozzle and out to the open atmosphere at supersonic spee...

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A Numerical Method for Two-Phase Flow Consisting of Separate Compressible and Incompressible Regions

Cited by 130 publications

References 34 publications

A level set approach to Eulerian–Lagrangian coupling

A level set approach to Eulerian–Lagrangian coupling

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

Optimal Control of Shock Wave Attenuation using Liquid Water Droplets with Application to Ignition Overpressure in Launch Vehicles

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