The Ghost Fluid Method for Deflagration and Detonation Discontinuities

Fedkiw, Ronald; Aslam, Tariq D.; Xu, Shaojie

doi:10.1006/jcph.1999.6320

Cited by 155 publications

(107 citation statements)

References 25 publications

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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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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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“…The conditions (14) imply in particular that (13) is a weak solution of (1). Now, fixing a state (ρ l , m l ) ∈ A × R we can determine the set of states (ρ r , m r ) hat can be connected to (ρ l , m l ) ∈ A × R by a shock wave, the so called Rankine-Hugoniot set for (ρ l , m l ).…”

Section: Rankine-hugoniot Conditions Shock Waves and Phase Transitionsmentioning

confidence: 99%

“…To circumvent this difficulty we suggest a ghost-fluid type algorithm, motivated but different from the algorithm in the seminal paper [13] (see [2,4,14,20,26] for other applications). The crucial analytical basis of the ghost fluid algorithm is the Riemann solver which has been developed in the first part of the paper (cf.…”

Section: Introductionmentioning

confidence: 99%

The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques

Merkle¹,

Rohde

2007

ESAIM: M2AN

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Abstract. Systems of mixed hyperbolic-elliptic conservation laws can serve as models for the evolution of a liquid-vapor fluid with possible sharp dynamical phase changes. We focus on the equations of ideal hydrodynamics in the isothermal case and introduce a thermodynamically consistent solution of the Riemann problem in one space dimension. This result is the basis for an algorithm of ghost fluid type to solve the sharp-interface model numerically. In particular the approach allows to resolve phase transitions sharply, i.e., without artificial smearing in the physically irrelevant elliptic region. Numerical experiments demonstrate the reliability of the method.Mathematics Subject Classification. 35M10, 76T10.

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“…For example the work of Fedkiw, et al [9] solves for single fluids separately by filling in "ghostfluid regions" with appropriate values that are consistent with the interface motion. Such methodologies can be extended to model "shocks" separating fluid states.…”

Section: Motivation and Backgroundmentioning

confidence: 99%

“…where the exact grid function u e j is defined in terms of the exact field solution u It can be shown that the discretization error is proportional to the truncation error which permits the discretization error to be written in a one-dimensional form as 9) where p corresponds to the order of the spatial discretization, q to the order of the temporal discretization, and H.O.T. indicates higher-order terms.…”

Section: Accuracy Assessmentmentioning

confidence: 99%

An assessment of semi-discrete central schemes for hyperbolic conservation laws.

Christon¹,

Robinson²,

Ketcheson³

2003

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High-resolution finite volume methods for solving systems of conservation laws have been widely embraced in research areas ranging from astrophysics to geophysics and aero-thermodynamics. These methods are typically at least second-order accurate in space and time, deliver non-oscillatory solutions in the presence of near discontinuities, e.g., shocks, and introduce minimal dispersive and diffusive effects. High-resolution methods promise to provide greatly enhanced solution methods for Sandia's mainstream shock hydrodynamics and compressible flow applications, and they admit the possibility of a generalized framework for treating multi-physics problems such as the coupled hydrodynamics, electro-magnetics and radiative transport found in zpinch physics. In this work, we describe initial efforts to develop a generalized "black-box" conservation law framework based on modern high-resolution methods and implemented in an object-oriented software framework. The framework is based on the solution of systems of general non-linear hyperbolic conservation laws using Godunov-type central schemes. In our initial 1 Keywords and Phrases: high-resolution, hyperbolic conservation laws, Godunov, semidiscrete, central schemes 2 Authors listed in alphabetic order.3 efforts, we have focused on central or central-upwind schemes that can be implemented with only a knowledge of the physical flux function and the minimal/maximal eigenvalues of the Jacobian of the flux functions, i.e., they do not rely on extensive Riemann decompositions. Initial experimentation with high-resolution central schemes suggests that contact discontinuities with the concomitant linearly degenerate eigenvalues of the flux Jacobian do not pose algorithmic difficulties. However, central schemes can produce significant smearing of contact discontinuities and excessive dissipation for rotational flows. Comparisons between "black-box" central schemes and the piecewiseparabolic method (PPM), which relies heavily on a Riemann decomposition, shows that roughly equivalent accuracy can be achieved for the same computational cost with both methods. However, PPM clearly outperforms the central schemes in terms of accuracy at a given grid resolution and the cost of additional complexity in the numerical flux functions. Overall we have observed that the finite volume schemes, implemented within a well-designed framework, are extremely efficient with (potentially) very low memory storage. Finally, we have found by computational experiment that second and third-order strong-stability preserving (SSP) time integration methods with the number of stages greater than the order provide a useful enhanced stability region. However, we observe that non-SSP and non-optimal SSP schemes with SSP factors less than one can still be very useful if used with time-steps below the standard CFL limit. The "well-designed" integration schemes that we have examined appear to perform well in all instances where the time step is maintained below the standard physical CFL limit. Acknowled...

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The Ghost Fluid Method for Deflagration and Detonation Discontinuities

Cited by 155 publications

References 25 publications

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

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

The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques

An assessment of semi-discrete central schemes for hyperbolic conservation laws.

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