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

Title: A robust and efficient finite volume method for compressible inviscid and viscous two-phase flows [A robust and efficient finite volume method for compressible viscous two-phase flows]

Journal Article · · Journal of Computational Physics
ORCiD logo [1]; ORCiD logo [1]
  1. North Carolina State Univ., Raleigh, NC (United States)
+ Show Author Affiliations

A robust and efficient density-based finite volume method is developed for solving the six-equation single pressure system of two-phase flows at all speeds on hybrid unstructured grids. Unlike conventional approaches where an expensive exact Riemann solver is normally required for computing numerical fluxes at the two-phase interfaces in addition to AUSM-type fluxes for single-phase interfaces in order to maintain stability and robustness in cases involving interactions of strong pressure and void-fraction discontinuities, a volume-fraction coupling term for the AUSM+-up fluxes is introduced in this work to impart the required robustness without the need of the exact Riemann solver. The resulting method is significantly less expensive in regions where otherwise the Riemann solver would be invoked. A transformation from conservative variables to primitive variables is presented and the primitive variables are then solved in the implicit method in order for the current finite volume method to be able to solve, effectively and efficiently, low Mach number flows in traditional multiphase applications, which otherwise is a great challenge for the standard density-based algorithms. Here, a number of benchmark test cases are presented to assess the performance and robustness of the developed finite volume method for both inviscid and viscous two-phase flow problems. The numerical results indicate that the current density-based method provides an attractive and viable alternative to its pressure-based counterpart for compressible two-phase flows at all speeds.

Research Organization:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); UT-Battelle LLC/ORNL, Oak Ridge, TN (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC05-00OR22725
OSTI ID:
1543562
Alternate ID(s):
OSTI ID: 1532775
Journal Information:
Journal of Computational Physics, Vol. 371, Issue C; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 16 works
Citation information provided by
Web of Science

References (40)

On the computation of multi-material flows using ALE formulation journal February 2004
A pressure-correction scheme for convection-dominated incompressible flows with discontinuous velocity and continuous pressure journal February 2011
A hybrid reconstructed discontinuous Galerkin and continuous Galerkin finite element method for incompressible flows on unstructured grids journal October 2016
NEPTUNE: A New Software Platform for Advanced Nuclear Thermal Hydraulics journal July 2007
Fully-implicit orthogonal reconstructed Discontinuous Galerkin method for fluid dynamics with phase change journal January 2016
On physics-based preconditioning of the Navier–Stokes equations journal December 2009
An Approximate Linearized Riemann Solver for a Two-Fluid Model journal March 1996
A robust and accurate approach to computing compressible multiphase flow: Stratified flow model and AUSM+-up scheme journal July 2007
How to Solve Compressible Multifluid Equations: a Simple, Robust, and Accurate Method journal September 2008
Extension and Comparative Study of AUSM-Family Schemes for Compressible Multiphase Flow Simulations journal September 2014
On the quest for a hyperbolic effective-field model of disperse flows journal August 2013
The influence of interfacial pressure forces on the character of two-phase flow model equations journal December 1977
How to Prevent Pressure Oscillations in Multicomponent Flow Calculations: A Quasi Conservative Approach journal April 1996
A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows journal April 1999
Numerical methods for nonconservative hyperbolic systems: a theoretical framework. journal January 2006
Simple and robust HLLC extensions of two-fluid AUSM for multiphase flow computations journal September 2014
Computations of two-fluid models based on a simple and robust hybrid primitive variable Riemann solver with AUSMD journal March 2016
Simulations of the shock waves and cavitation bubbles during a three-dimensional high-speed droplet impingement based on a two-fluid model journal August 2016
Ransom test results from various two-fluid schemes: Is enforcing hyperbolicity a thermodynamically consistent option? journal May 2016
A multiphase model for compressible granular–gaseous flows: formulation and initial tests journal January 2016
A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials journal November 1986
A Simple Method for Compressible Multifluid Flows journal January 1999
A multiphase model for compressible flows with interfaces, shocks, detonation waves and cavitation journal March 2001
Discrete equations for physical and numerical compressible multiphase mixtures journal April 2003
The physical closure laws in the CATHARE code journal December 1990
The effect of virtual mass on the numerical stability of accelerating two-phase flows journal August 1980
The analysis of virtual mass effects in two-phase flow journal August 1979
A vertex-based hierarchical slope limiter for <mml:math altimg="si27.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>p</mml:mi></mml:math>-adaptive discontinuous Galerkin methods journal April 2010
A sequel to AUSM, Part II: AUSM+-up for all speeds journal May 2006
A simple method to compute standard two-fluid models journal October 2005
Hyperbolic relaxation models for granular flows journal January 2010
Low-Diffusion Flux-Splitting Methods for Flows at All Speeds journal September 1998
High Order Extensions of Roe Schemes for Two-Dimensional Nonconservative Hyperbolic Systems journal October 2008
A Simple Extension of the Osher Riemann Solver to Non-conservative Hyperbolic Systems journal July 2010
A MUSTA Scheme for a Nonconservative Two-Fluid Model journal January 2009
An accurate, fast, matrix-free implicit method for computing unsteady flows on unstructured grids journal February 2001
A Fast, Matrix-free Implicit Method for Compressible Flows on Unstructured Grids journal November 1998
On the extension of the AUSM+ scheme to compressible two-fluid models journal July 2003
Numerical investigation of collapsing cavity arrays journal May 2012
Adaptive characteristics-based matching for compressible multifluid dynamics journal April 2006

Cited By (4)

A high-order accurate AUSM$$^+$$-up approach for simulations of compressible multiphase flows with linear viscoelasticity journal January 2019
Uncertainty quantification of shock–bubble interaction simulations journal February 2019
An enhanced AUSM $$^{+}$$ + -up scheme for high-speed compressible two-phase flows on hybrid grids journal September 2018
A reconstructed discontinuous Galerkin method for multi‐material hydrodynamics with sharp interfaces journal January 2020

Figures / Tables (34)

Figure 1(p. 26)figure Figure 1
Figure 2(p. 26)figure Figure 2
Figure 3(p. 27)figure Figure 3
Figure 4(p. 27)figure Figure 4
Figure 5(p. 28)figure Figure 5
Figure 6(p. 28)figure Figure 6
Figure 7(p. 29)figure Figure 7
Figure 8(p. 30)figure Figure 8
Figure 9(p. 30)figure Figure 9
Figure 10(p. 31)figure Figure 10
Figure 11(p. 31)figure Figure 11
Figure 12(p. 32)figure Figure 12
Figure 13(p. 33)figure Figure 13
Figure 14(p. 33)figure Figure 14
Figure 15(p. 34)figure Figure 15
Figure 16(p. 37)figure Figure 16
Figure 17(p. 37)figure Figure 17
Figure 18(p. 37)figure Figure 18
Figure 19(p. 40)figure Figure 19
Figure 20(p. 40)figure Figure 20
Figure 21(p. 40)figure Figure 21
Figure 22(p. 41)figure Figure 22
Figure 23(p. 41)figure Figure 23
Figure 24(p. 41)figure Figure 24
Figure 25(p. 42)figure Figure 25
Figure 26(p. 42)figure Figure 26
Figure 27(p. 42)figure Figure 27
Figure 28(p. 43)figure Figure 28
Figure 29(p. 44)figure Figure 29
Table 1(p. 44)table Table 1
Figure 30(p. 45)figure Figure 30
Figure 31(p. 47)figure Figure 31
Figure 32(p. 47)figure Figure 32
Figure 33(p. 47)figure Figure 33

Similar Records

Related Subjects

97 MATHEMATICS AND COMPUTING
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Computer Science
Physics
Two-fluid model
Six equation
All-speed methods