Linear and nonlinear analysis of an unstable, but well-posed, one-dimensional two-fluid model for two-phase flow based on the inviscid Kelvin–Helmholtz instability

Efficient simulation of one-dimensional two-phase flow with a high-order h-adaptive space-time Discontinuous Galerkin method

“…The model is similar to the models used by Liao et al [6] and Fullmer et al [8] . A difference worth noting is the hydrostatic pressure term p av, β in the momentum Eq.…”

Simplified 1D Incompressible Two-Fluid Model with Artificial Diffusion for Slug Flow Capturing in Horizontal and Nearly Horizontal Pipes

“…To partially overcome this issue, Issa and Kempf [11] used grid diffusivity to dampen the short wavelengths' growth; this approach, however, does not ensure grid independence for every flow conditions since, as the grid is refined, the system is more sensitive to short wavelengths' instabilities. Fullmer et al [21] propose to consider the viscous stress term (i.e., Reynolds stress) in the momentum equation and to account for the surface tension (see also [22]); the latter approach does not have a straightforward implementation because of the third-order derivative. Again, it would be possible to render the system hyperbolic with a physically-meaningful term such as the virtual mass, but this kind of description was developed mainly for dispersed flow; thus, in this work, this is not a viable strategy because we focus mainly on stratified and slug flow regimes.…”

Optimization of the Interfacial Shear Stress and Assessment of Closure Relations for Horizontal Viscous Oil-Gas Flows in the Stratified and Slug Regimes

“…For testing the hyperbolicity of the 1D Two-Fluid Model, the most basic test is to perform the analysis of its characteristics, as performed by Issa & Kempf (2003). An alternative manner is through a linear stability analysis, particularly by calculating the growth rate of small wavelength instabilities, as done by Fullmer et al (2014). This option is especially advantageous for analyzing the effects of higher-order terms, because reducing the system of equations to first-order for performing its characteristics analysis might lead to issues, as shown by Montini (2011).…”

“…There are several methods to regularize, that is, to recover hyperbolicity of the 1D Two-Fluid Model, such as through a model for the dynamic pressure (Bestion, 1990), by artificially increasing the numerical and/or physical momentum diffusion of the model (Fullmer et al, 2014), or by adding the volume fraction conservation equation and using two pressures as variables together with pressure relaxation effects (Baer & Nunziato, 1986;Saurel & Abgrall, 1999;Flatten & Lund, 2011;Ferrari et al, 2017). Pasqualette et al (2017) showed that increasing interfacial shear stress is also capable of stabilizing (and regularize) the 1D TwoFluid Model in the Regime Capturing Methodology framework.…”

“…Pasqualette et al (2017) showed that increasing interfacial shear stress is also capable of stabilizing (and regularize) the 1D TwoFluid Model in the Regime Capturing Methodology framework. Other traditional regularization methods are: adding artificial axial diffusion to the mass conservation equations (Fullmer et al, 2014) and correctly modelling the momentum distribution parameters (Song, 2003). More details on the regularizing methods just cited will be provided in a later chapter of this work.…”