NDLI: CFL-Violating Numerical Schemes for a Two-Fluid Model

Content Provider	Springer Nature Link
Author	Evje, Steinar Flåtten, Tore
Copyright Year	2005
Abstract	In this paper we propose a class of linearly implicit numerical schemes for a two-phase flow model, allowing for violation of the CFL-criterion for all waves. Based on the Weakly Implixit Mixture Flux (WIMF) approach [SIAM J. Sci. Comput., 26 (2005), pp. 1449–1484], we here develop an extension denoted as Strongly Implicit Mixture Flux (SIMF). Whereas the WIMF schemes are restricted by a weak CFL condition which relates time steps to the fluid velocity, the SIMF schemes are able to break the CFL conditions corresponding to both the sonic and advective velocities. The schemes possess some desirable features compared to current industrial pressure-based codes. They allow for sequential updating of the momentum and mass variables on a nonstaggered grid by solving two sparse linear systems. The schemes are conservative in all convective fluxes and consistency between the mass variables and pressure is formally maintained. Numerical experiments are presented to shed light on the inherent differences between the WIMF and SIMF families of schemes. In particular, we demonstrate that the WIMF scheme is able to give an exact resolution of a moving contact discontinuity. The SIMF schemes do not possess the “exact resolution” property of WIMF, however, the ability to take larger time steps can be exploited so that more efficient calculations can be made when accurate resolution of sharp fronts is not essential, e.g. to calculate steady state solutions.
Starting Page	83
Ending Page	114
Page Count	32
File Format	PDF
ISSN	08857474
Journal	Journal of Scientific Computing
Volume Number	29
Issue Number	1
e-ISSN	15737691
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	2005-12-13
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Two-phase flow two-fluid model hyperbolic system of conservation laws flux splitting implicit scheme Liquid-gas two-phase flows, bubbly flows Existence, uniqueness, and regularity theory Stability and convergence of numerical methods Conservation laws Mathematical and Computational Physics ApplicationMathematics/Computational Methods of Engineering Computational Mathematics and Numerical Analysis Algorithms
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Engineering Computational Theory and Mathematics Computational Mathematics Numerical Analysis Software

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