scholarly journals Multiscale Time-Splitting Strategy for Multiscale Multiphysics Processes of Two-Phase Flow in Fractured Media

2011 ◽  
Vol 2011 ◽  
pp. 1-24 ◽  
Author(s):  
Jisheng Kou ◽  
Shuyu Sun ◽  
Bo Yu
Keyword(s):  
Porous Media ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Step Size ◽  
Time Step ◽  
Two Phase ◽  
Time Step Size ◽  
Multi Scale ◽  
Rapid Changes ◽  
Time Splitting

The temporal discretization scheme is one important ingredient of efficient simulator for two-phase flow in the fractured porous media. The application of single-scale temporal scheme is restricted by the rapid changes of the pressure and saturation in the fractured system with capillarity. In this paper, we propose a multi-scale time splitting strategy to simulate multi-scale multi-physics processes of two-phase flow in fractured porous media. We use the multi-scale time schemes for both the pressure and saturation equations; that is, a large time-step size is employed for the matrix domain, along with a small time-step size being applied in the fractures. The total time interval is partitioned into four temporal levels: the first level is used for the pressure in the entire domain, the second level matching rapid changes of the pressure in the fractures, the third level treating the response gap between the pressure and the saturation, and the fourth level applied for the saturation in the fractures. This method can reduce the computational cost arisen from the implicit solution of the pressure equation. Numerical examples are provided to demonstrate the efficiency of the proposed method.

scholarly journals Diffuse-interface two-phase flow models with different densities: A new quasi-incompressible form and a linear energy-stable method

2018 ◽  
Vol 28 (04) ◽  
pp. 733-770 ◽  
Author(s):  
M. Shokrpour Roudbari ◽  
G. Şimşek ◽  
E. H. van Brummelen ◽  
K. G. van der Zee
Keyword(s):  
Two Phase Flow ◽  
Linear Method ◽  
Diffuse Interface ◽  
Integration Scheme ◽  
Phase Flow ◽  
Time Step ◽  
Two Phase ◽  
Time Step Size ◽  
Mixture Density ◽  
Energy Stable

While various phase-field models have recently appeared for two-phase fluids with different densities, only some are known to be thermodynamically consistent, and practical stable schemes for their numerical simulation are lacking. In this paper, we derive a new form of thermodynamically-consistent quasi-incompressible diffuse-interface Navier–Stokes–Cahn–Hilliard model for a two-phase flow of incompressible fluids with different densities. The derivation is based on mixture theory by invoking the second law of thermodynamics and Coleman–Noll procedure. We also demonstrate that our model and some of the existing models are equivalent and we provide a unification between them. In addition, we develop a linear and energy-stable time-integration scheme for the derived model. Such a linearly-implicit scheme is nontrivial, because it has to suitably deal with all nonlinear terms, in particular those involving the density. Our proposed scheme is the first linear method for quasi-incompressible two-phase flows with non-solenoidal velocity that satisfies discrete energy dissipation independent of the time-step size, provided that the mixture density remains positive. The scheme also preserves mass. Numerical experiments verify the suitability of the scheme for two-phase flow applications with high density ratios using large time steps by considering the coalescence and breakup dynamics of droplets including pinching due to gravity.

scholarly journals Adaptive time-splitting scheme for two-phase flow in heterogeneous porous media

2017 ◽  
Vol 1 (3) ◽  
pp. 182-189 ◽  
Author(s):  
Mohamed F. El-Amin ◽  
Jisheng Kou ◽  
Shuyu Sun ◽  
Amgad Salama
Keyword(s):  
Porous Media ◽  
Two Phase Flow ◽  
Heterogeneous Porous Media ◽  
Phase Flow ◽  
Splitting Scheme ◽  
Two Phase ◽  
Adaptive Time ◽  
Time Splitting

A Numerical Study of BWR Steam Separator

2002 ◽  
Author(s):  
Haruo Terasaka ◽  
Sensuke Shimizu
Keyword(s):  
Transient Flow ◽  
Numerical Study ◽  
Fluid Model ◽  
Flow Analysis ◽  
Phase Flow ◽  
Step Size ◽  
Time Step ◽  
Two Phase ◽  
Time Step Size ◽  
Steam Separator

An advanced numerical method based on two-fluid model of two-phase flow has been developed to simulate the swirling gas-liquid flow and the phase separation process in a Boiling Water Reactor separator. The goal is to correctly predict the performance of operating steam separator as well as new designs. The solution method present here is an extension of SIMPLEST scheme, a fully implicit scheme for single-phase flow analysis. It is robust and unconditionally stable, therefore enable us to use very large time step size. This feature is suitable for steady and/or slow transient flow analyses. Furthermore, it enhances numerical stability during rapid transient calculations. By employing this method, separator hydrodynamics around swirler were calculated.

A Numerical Simulation of Swirling Two-Phase Flow in BWR Steam-Water Separator and Its Optimization

2003 ◽  
Author(s):  
Haruo Terasaka ◽  
Sensuke Shimizu ◽  
Minoru Kawahara
Keyword(s):  
Transient Flow ◽  
Fluid Model ◽  
Flow Analysis ◽  
Phase Flow ◽  
Step Size ◽  
Time Step ◽  
Two Phase ◽  
Time Step Size ◽  
Fully Implicit ◽  
Water Separator

An advanced numerical method based on the two-fluid model has been developed. The solution method presented here is an extension of the SIMPLEST scheme, a fully implicit scheme for single-phase flow analysis. It is robust and unconditionally stable, and therefore it enables us to use a very large time step size. This feature is suitable for steady and/or slow transient flow analyses. Furthermore, it enhances numerical stability during rapid transient calculations. By using this method, swirling gas-liquid flow in a steam-water separator of Boiling Water Reactors (BWRs) was calculated and the hydrodynamics characteristics were investigated for optimization.

scholarly journals Numerical Fractional-Calculus Model for Two-Phase Flow in Fractured Media

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Wenwen Zhong ◽  
Changpin Li ◽  
Jisheng Kou
Keyword(s):  
Porous Media ◽  
Large Time ◽  
Two Phase Flow ◽  
Time Derivative ◽  
Fractured Porous Media ◽  
Phase Flow ◽  
Petroleum Reservoir ◽  
Time Step ◽  
Two Phase ◽  
Large Time Step

Numerical simulation of two-phase flow in fractured porous media is an important topic in the subsurface flow, environmental problems, and petroleum reservoir engineering. The conventional model does not work well in many cases since it lacks the memory property of fracture media. In this paper, we develop a new numerical formulation with fractional time derivative for two-phase flow in fractured porous media. In the proposed formulation, the different fractional time derivatives are applied to fracture and matrix regions since they have different memory properties. We further develop a two-level time discrete method, which uses a large time step for the pressure and a small time step size for the saturation. The pressure equation is solved implicitly in each large time step, while the saturation is updated by an explicit fractional time scheme in each time substep. Finally, the numerical tests are carried out to demonstrate the effectiveness of the proposed numerical model.

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