skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Diffuse-Interface Capturing Methods for Compressible Two-Phase Flows

Journal Article · · Annual Review of Fluid Mechanics
 [1];  [2]
  1. Aix-Marseille Univ., Marseille (France); Univ. of Institute of France, Paris (France)
  2. Univ. of Illinois at Urbana-Champaign, Urbana, IL (United States)

Simulation of compressible flows became a routine activity with the appearance of shock-/contact-capturing methods. These methods can determine all waves, particularly discontinuous ones. However, additional difficulties may appear in two-phase and multimaterial flows due to the abrupt variation of thermodynamic properties across the interfacial region, with discontinuous thermodynamical representations at the interfaces. To overcome this difficulty, researchers have developed augmented systems of governing equations to extend the capturing strategy. These extended systems, reviewed here, are termed diffuse-interface models, because they are designed to compute flow variables correctly in numerically diffused zones surrounding interfaces. In particular, they facilitate coupling the dynamics on both sides of the (diffuse) interfaces and tend to the proper pure fluid–governing equations far from the interfaces. This strategy has become efficient for contact interfaces separating fluids that are governed by different equations of state, in the presence or absence of capillary effects, and with phase change. As a result, more sophisticated materials than fluids (e.g., elastic–plastic materials) have been considered as well.

Research Organization:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
NA0002382
OSTI ID:
1434325
Journal Information:
Annual Review of Fluid Mechanics, Vol. 50, Issue 1; ISSN 0066-4189
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 82 works
Citation information provided by
Web of Science

References (72)

How to Prevent Pressure Oscillations in Multicomponent Flow Calculations: A Quasi Conservative Approach journal April 1996
Discrete equations for physical and numerical compressible multiphase mixtures journal April 2003
Droplet vaporization model for spray combustion calculations journal September 1989
A Five-Equation Model for the Simulation of Interfaces between Compressible Fluids journal September 2002
Diffuse-Interface Methods in Fluid Mechanics journal January 1998
Level Set Methods Applied to Modeling Detonation Shock Dynamics journal July 1996
A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials journal November 1986
Two-phase modeling of deflagration-to-detonation transition in granular materials: A critical examination of modeling issues journal February 1999
A continuum method for modeling surface tension journal June 1992
Free Energy of a Nonuniform System. I. Interfacial Free Energy journal February 1958
A simple and fast phase transition relaxation solver for compressible multicomponent two-phase flows journal June 2017
A simple phase transition relaxation solver for liquid–vapor flows
  • Chiapolino, Alexandre; Boivin, Pierre; Saurel, Richard
  • International Journal for Numerical Methods in Fluids, Vol. 83, Issue 7 https://doi.org/10.1002/fld.4282
journal August 2016
Sharpening diffuse interfaces with compressible fluids on unstructured meshes journal July 2017
FORCE schemes on unstructured meshes II: Non-conservative hyperbolic systems journal January 2010
Solid–fluid diffuse interface model in cases of extreme deformations journal September 2009
A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method) journal July 1999
Runge–Kutta discontinuous Galerkin method for the approximation of Baer and Nunziato type multiphase models journal June 2012
A simple HLLC-type Riemann solver for compressible non-equilibrium two-phase flows journal April 2015
Three-Dimensional Front Tracking journal May 1998
Uniformly high order accurate essentially non-oscillatory schemes, III journal August 1987
On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws journal January 1983
Vortex dynamics in 3D shock-bubble interaction journal September 2013
An arbitrary Lagrangian-Eulerian computing method for all flow speeds journal March 1974
Volume of fluid (VOF) method for the dynamics of free boundaries journal January 1981
Numerical simulations of non-spherical bubble collapse journal June 2009
Two-phase modeling of deflagration-to-detonation transition in granular materials: Reduced equations journal October 2001
Pressure relaxation procedures for multiphase compressible flows journal January 2005
Quantitative numerical and experimental studies of the shock accelerated heterogeneous bubbles motion journal April 2007
Liquid and liquid–gas flows at all speeds journal December 2013
Towards the direct numerical simulation of nucleate boiling flows journal November 2014
The Noble-Abel Stiffened-Gas equation of state journal April 2016
Wave Propagation Algorithms for Multidimensional Hyperbolic Systems journal March 1997
Finite Volume Methods for Hyperbolic Problems book January 2002
A New Family of High Order Unstructured MOOD and ADER Finite Volume Schemes for Multidimensional Systems of Hyperbolic Conservation Laws journal September 2014
A Hierarchy of Relaxation Models for Two-Phase Flow journal January 2012
Proposition de méthodes et modèles eulériens pour les problèmes à interfaces entre fluides compressibles en présence de transfert de chaleur journal March 2002
A five equation reduced model for compressible two phase flow problems journal January 2005
Multi-solid and multi-fluid diffuse interface model: Applications to dynamic fracture and fragmentation journal August 2015
A conservative level set method for two phase flow II journal July 2007
Upwind difference schemes for hyperbolic systems of conservation laws journal May 1982
A compressible flow model with capillary effects journal October 2005
A relaxation-projection method for compressible flows. Part II: Artificial heat exchanges for multiphase shocks journal August 2007
Modelling detonation waves in condensed energetic materials: multiphase CJ conditions and multidimensional computations journal July 2009
Approximate Riemann solvers, parameter vectors, and difference schemes journal October 1981
11 PFLOP/s simulations of cloud cavitation collapse
  • Rossinelli, Diego; Koumoutsakos, Petros; Hejazialhosseini, Babak
  • Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis on - SC '13 https://doi.org/10.1145/2503210.2504565
conference January 2013
A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows journal April 1999
A Simple Method for Compressible Multifluid Flows journal January 1999
A general formulation for cavitating, boiling and evaporating flows journal April 2016
Modelling compressible dense and dilute two-phase flows journal June 2017
A relaxation-projection method for compressible flows. Part I: The numerical equation of state for the Euler equations journal May 2007
A multiphase model with internal degrees of freedom: application to shock–bubble interaction journal November 2003
Symmetric model of compressible granular mixtures with permeable interfaces journal December 2014
Shock jump relations for multiphase mixtures with stiff mechanical relaxation journal January 2007
Modelling phase transition in metastable liquids: application to cavitating and flashing flows journal June 2008
Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures journal March 2009
Direct Numerical Simulation of Free-Surface and Interfacial flow journal January 1999
Multi-phase simulation of ammonium nitrate emulsion detonations journal September 2013
L EVEL S ET M ETHODS FOR F LUID I NTERFACES journal January 2003
Efficient implementation of essentially non-oscillatory shock-capturing schemes journal August 1988
Nonlinear preconditioning for efficient and accurate interface capturing in simulation of multicomponent compressible flows journal November 2014
An interface capturing method for the simulation of multi-phase compressible flows journal September 2010
An Efficient Shock-Capturing Algorithm for Compressible Multicomponent Problems journal May 1998
An Eulerian interface sharpening algorithm for compressible two-phase flow: The algebraic THINC approach journal July 2014
A diffuse interface model with immiscibility preservation journal November 2013
Growth-and-collapse dynamics of small bubble clusters near a wall journal June 2015
HLLC-type Riemann solver for the Baer–Nunziato equations of compressible two-phase flow journal May 2010
Riemann Solvers and Numerical Methods for Fluid Dynamics book January 2009
Restoration of the contact surface in the HLL-Riemann solver journal July 1994
Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method journal July 1979
A Method for the Numerical Calculation of Hydrodynamic Shocks journal March 1950
Modeling phase transition for compressible two-phase flows applied to metastable liquids journal April 2010
Positivity-preserving high order finite difference WENO schemes for compressible Euler equations journal March 2012

Cited By (8)

Modeling Heavy-Gas Dispersion in Air with Two-Layer Shallow Water Equations text January 2021
Numerical modelling of shock-bubble interactions using a pressure-based algorithm without Riemann solvers journal June 2019
Numerical modelling of shock-bubble interactions using a pressure-based algorithm without Riemann solvers text January 2019
Small-scale kinematics of two-phase flows: identifying relaxation processes in separated- and disperse-phase flow models journal August 2019
A Review of Models for Bubble Clusters in Cavitating Flows journal November 2018
High order moment model for polydisperse evaporating sprays towards interfacial geometry text January 2016
Entropy stable, robust and high-order DGSEM for the compressible multicomponent Euler equations journal November 2021
Kinetic modeling of multiphase flow based on simplified Enskog equation text January 2020

Figures / Tables (9)


Similar Records

An oscillation free shock-capturing method for compressible van der Waals supercritical fluid flows
Journal Article · Wed Feb 01 00:00:00 EST 2017 · Journal of Computational Physics · OSTI ID:1434325

A relaxation-projection method for compressible flows. Part I: The numerical equation of state for the Euler equations
Journal Article · Tue May 01 00:00:00 EDT 2007 · Journal of Computational Physics · OSTI ID:1434325

A compressible flow model with capillary effects
Journal Article · Mon Oct 10 00:00:00 EDT 2005 · Journal of Computational Physics · OSTI ID:1434325