### Citations

195 |
Termo-Fluid Dynamic Theory of TwoPhase Flow, Direction des Etudes et Recherches d`electricé de France, Eyrolles, Paris. wnloaded From: https://proceedings.asmedigitalcollection.asme.org on 06/17/2019
- Ishii
- 1975
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Citation Context ...ast two phases or fluids and the interactions due to exchange of mass, momentum and energy. A large class of models are based on the continuum theory and make use of average quantities [9], [3], [4], =-=[5]-=- inside each control volume allowing us to know the amount of each phase in the volume but not the position of the interphases. Models in current use, when neglecting dissipative effects, consist of n... |

137 |
Mathematical modeling of two-phase flow,”
- Drew
- 1983
(Show Context)
Citation Context ...at least two phases or fluids and the interactions due to exchange of mass, momentum and energy. A large class of models are based on the continuum theory and make use of average quantities [9], [3], =-=[4]-=-, [5] inside each control volume allowing us to know the amount of each phase in the volume but not the position of the interphases. Models in current use, when neglecting dissipative effects, consist... |

122 |
Theory of Multicomponent Fluids.
- Drew, Passman
- 1998
(Show Context)
Citation Context ...r of at least two phases or fluids and the interactions due to exchange of mass, momentum and energy. A large class of models are based on the continuum theory and make use of average quantities [9], =-=[3]-=-, [4], [5] inside each control volume allowing us to know the amount of each phase in the volume but not the position of the interphases. Models in current use, when neglecting dissipative effects, co... |

92 |
A Multiphase Godunov method for compressible Multifluid and Multiphase flows,
- SAUREL, ABGRALL
- 1999
(Show Context)
Citation Context ...be defined once a conservative form of the equations exists. Almost all the models in literature have non-conservative form due to the interface interaction. Examples include the Saurel-Abgrall model =-=[8]-=- and the Baer-Nunziato model [2]. See also [9]. We note here that conservative hyperbolic models have recently been proposed [7], which are formulated in terms of parameters of state for the mixture. ... |

80 |
Two-phase flow : Models and methods,
- STEWART, WENDROFF
- 1984
(Show Context)
Citation Context ...havior of at least two phases or fluids and the interactions due to exchange of mass, momentum and energy. A large class of models are based on the continuum theory and make use of average quantities =-=[9]-=-, [3], [4], [5] inside each control volume allowing us to know the amount of each phase in the volume but not the position of the interphases. Models in current use, when neglecting dissipative effect... |

55 |
On the Relation between Upwinddifferencing Schemes of Godunov, Enquist-Osher,
- Leer
- 1984
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Citation Context ...he ADER interface state to be used in formula (42), where the coefficient matrix is taking as ( 1 ( Âi = A W 1 i− 2 2 5.2 The MUSCL Hancock method i+ 1 2 + W i+ 1 2 i+ 1 2 ) ) . (49) In this approach =-=[15]-=- data reconstruction is performed using piece wise linear functions, see (43), and boundary extrapolated values are evolved by half a time step and then used as initial data for a a piece-wise constan... |

28 |
Towards very high order Godunov schemes.
- Toro, Millington, et al.
- 2001
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Citation Context ...usual CFL or Courant number coefficient. The second order schemes are: an ADER second order scheme and the MUSCL Hancock scheme. 5.1 A second order ADER scheme To construct a second-order ADER scheme =-=[11]-=-, we assume a piece-linear reconstruction and consider the piece-wise linear Riemann problem ∂tW + A(W)∂xW = 0 ⎫ ⎧ ⎪⎨ WL(x) ≡ W W(x, 0) = ⎪⎩ n WR(x) ≡ W n i + (x−xi) ∆x ∆i i+1 + (x−xi+1) ∆x ∆i+1 The s... |

27 |
Quasilinear hyperbolic systems and waves
- Jeffrey
- 1976
(Show Context)
Citation Context ...) pi − pl αlρl ⎥ ⎦ 0 0 0 0 λ 3 Eigenstructure and generalized Riemann invariants In this section we establish the eigenstructure of the systems (9), (14) and derive the generalized Riemann invariants =-=[6]-=-; these will be utilized in section 4 for finding an approximate solution to the Riemann problem. For both formulations (9), (14) the eigenvalues are λ1 = ul − al, λ2 = ug − ag, λ3 = λ, λ4 = ug + ag, ... |

15 |
The Riemann problem for the Baer– Nunziato two-phase flow model
- Andrianov, Warnecke
(Show Context)
Citation Context ... solution indicates that this is sufficiently accurate for use in the construction of upwind numerical methods. We note here that our theoretical solution is direct, unlike that presented by Adrianov =-=[1]-=- for the more complicated Baer-Nunziato model. Our Riemann solver is complete, in that it accounts for all waves present in the eigenstructure of the exact solution. Our solver is also non linear and ... |

11 |
A Two-Phase Mixture Theory for the the Deflagration to Detonation Transition (DDT) in Reactive Granular
- Baer, Nunziato
- 1986
(Show Context)
Citation Context ...orm of the equations exists. Almost all the models in literature have non-conservative form due to the interface interaction. Examples include the Saurel-Abgrall model [8] and the Baer-Nunziato model =-=[2]-=-. See also [9]. We note here that conservative hyperbolic models have recently been proposed [7], which are formulated in terms of parameters of state for the mixture. Given that most models in curren... |

5 | Compressible two-phase flows: two-pressure models and numerical methods
- 37Romenski, Toro
(Show Context)
Citation Context ...to the interface interaction. Examples include the Saurel-Abgrall model [8] and the Baer-Nunziato model [2]. See also [9]. We note here that conservative hyperbolic models have recently been proposed =-=[7]-=-, which are formulated in terms of parameters of state for the mixture. Given that most models in current use are in non-conservative form, it is of interest to develop numerical methodology that can ... |

4 |
conservative and adaptive schemes for hyperbolic conservation laws, in Numerical Methods for Wave Propagation (Manchester 95), edited by
- Toro, Primitive
- 1998
(Show Context)
Citation Context ...control spurious oscillations near large gradients of the solution. The non-conservative schemes are constructed on the basis of an extension of the finite volume approach to non-conservative systems =-=[13]-=-, [12]. The schemes have the form W n+1 i = W n i − ∆t ∆x Âi [ W 1 i+ 2 − W i− 1 2 ] , (42) where W n i is a spatial integral average within volume, or cell, i of length ∆x, at time level n; the coeff... |

3 |
primitive centred schemes for hyperbolic systems
- Toro, Siviglia
- 2003
(Show Context)
Citation Context ...l spurious oscillations near large gradients of the solution. The non-conservative schemes are constructed on the basis of an extension of the finite volume approach to non-conservative systems [13], =-=[12]-=-. The schemes have the form W n+1 i = W n i − ∆t ∆x Âi [ W 1 i+ 2 − W i− 1 2 ] , (42) where W n i is a spatial integral average within volume, or cell, i of length ∆x, at time level n; the coefficient... |

2 |
Solvers and Numerical Methods for Fluid Dynamics, Second Edition
- Riemann
- 1999
(Show Context)
Citation Context ...racteristic fields give rise to rarefaction waves. We call the approximation, the four-rarefaction approximation, and is an extension of the two-rarefaction approximation in single-phase gas dynamics =-=[14]-=-. The solution has close form and is actually exact in the case in which the Riemann problem has four rarefaction waves. For other cases our theoretical solution becomes an approximation. Careful asse... |