NDLI: A Roe-type scheme with low Mach number preconditioning for a two-phase compressible flow model with pressure relaxation

Content Provider	Springer Nature Link
Author	Pelanti, Marica Shyue, Keh Ming
Copyright Year	2016
Abstract	We describe two-phase compressible flows by a hyperbolic six-equation single-velocity two-phase flow model with stiff mechanical relaxation. In particular, we are interested in the simulation of liquid-gas mixtures such as cavitating flows. The model equations are numerically approximated via a fractional step algorithm, which alternates between the solution of the homogeneous hyperbolic portion of the system through Godunov-type finite volume schemes, and the solution of a system of ordinary differential equations that takes into account the pressure relaxation terms. When used in this algorithm, classical schemes such as Roe’s or HLLC prove to be very efficient to simulate the dynamics of transonic and supersonic flows. Unfortunately, these methods suffer from the well known difficulties of loss of accuracy and efficiency for low Mach number regimes encountered by upwind finite volume discretizations. This issue is particularly critical for liquid-gasmixtures due to the large and rapid variation in the flow of the acoustic impedance. To cure the problem of loss of accuracy at low Mach number, in this work we apply to our original Roe-type scheme for the two-phase flow model the Turkel’s preconditioning technique studied by Guillard–Viozat [Computers & Fluids, 28, 1999] for the Roe’s scheme for the classical Euler equations.We present numerical results for a two-dimensional liquid-gas channel flow test that show the effectiveness of the resulting Roe-Turkel method for the two-phase system.
Ending Page	669
Page Count	15
Starting Page	655
File Format	PDF
ISSN	16787544
e-ISSN	16787714
Journal	Bulletin of the Brazilian Mathematical Society
Issue Number	2
Volume Number	47
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-06-22
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Liquid-gas two-phase flows, bubbly flows Riemann solvers low Mach number preconditioning Theoretical, Mathematical and Computational Physics two-phase compressible flows mechanical relaxation finite volume schemes Mathematics liquid-gasmixtures Finite volume methods
Content Type	Text
Resource Type	Article
Subject	Mathematics

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