Numerical solution methods for multi-phase flow problems

2011 ◽  
pp. 497-602
Author(s):  
Nikolay Ivanov Kolev
Keyword(s):  
Numerical Solution ◽  
Phase Flow ◽  
Flow Problems ◽  
Numerical Solution Methods ◽  
Solution Methods ◽  
Multi Phase Flow ◽  
Multi Phase

A Second-Order IMEX Method for Multi-Phase Flow Problems

2016 ◽  
Vol 14 (05) ◽  
pp. 1750056 ◽  
Author(s):  
Samet Y. Kadioglu
Keyword(s):  
Surface Tension ◽  
Stokes Equations ◽  
Applied Mathematics ◽  
Second Order ◽  
Navier Stokes ◽  
Phase Flow ◽  
Flow Problems ◽  
Multi Phase Flow ◽  
Time Accuracy ◽  
Multi Phase

We present a fully second order IMplicit/EXplicit (IMEX) time integration technique for solving incompressible multi-phase flow problems. A typical incompressible multi-phase flow model consists of the Navier–Stokes equations plus an interface dynamics equation (e.g., the level set equation). Our IMEX strategy is applied to such a model in the following manner. The hyperbolic terms of the Navier–Stokes equations together with the interface dynamics equation are solved explicitly (Explicit Block) making use of the well-understood explicit numerical schemes [Leveque, R. J. [1998] Finite Volume Methods for Hyperbolic Problems, “Texts in Applied Mathematics”, (Cambridge University Press); Thomas, J. W. [1999] Numerical Partial Differential Equations II (Conservation Laws and Elliptic Equations), “Texts in Applied Mathematics” (Springer-Verlag, New York)]. On the other hand, the nonhyperbolic (stiff) parts of the flow equations are solved implicitly (Implicit Block) within the framework of the Jacobian-Free Newton Krylov (JFNK) method [Knoll, D. A. and Keyes, D. E. [2004] Jacobian-free Newton Krylov methods: A survey of approaches and applications. J. Comput. Phys. 193, 357–397; Saad, Y. [2003] Iterative Methods for Sparse Linear Systems (Siam); Kelley, C. T. [2003] Solving Nonlinear Equations with Newton’s Method (Siam)]. In our algorithm implementation, the explicit block is embedded in the implicit block in a way that it is always part of the nonlinear function evaluation. In this way, there exists a continuous interaction between the implicit and explicit algorithm blocks meaning that the improved solutions (in terms of time accuracy) at each nonlinear iteration are immediately felt by the explicit block and the improved explicit solutions are readily available to form the next set of nonlinear residuals. This continuous interaction between the two algorithm blocks results in an implicitly balanced algorithm in that all nonlinearities due to coupling of different time terms are converged with the desired numerical time accuracy. In other words, we obtain a self-consistent IMEX method that eliminates the possible order reductions in time convergence that is quite common in certain types of nonlinearly coupled systems. We remark that an incompressible multi-phase flow model can be a highly nonlinearly coupled system with the involvement of very stiff surface tension source terms. These kinds of flow problems are difficult to tackle numerically. In other words, highly nonlinear surface terms may remain unconverged leading to time inaccuracies or time order reductions to the first order even though the overall numerical scheme is designed as high order (second-order or higher) [Sussman, M. and Ohta, M. [2009] A stable and efficient method for treating surface tension in incompressible two-phase flow, SIAM J. Sci. Comput. 31(4), 2447–2471; Zheng, W., Zhu, B., Kim, B. and Fedkiw, R. [2015] A new incompressibility discretization for a hybrid particle MAC grid representation with surface tension, J. Comput. Phys. 280, 96–142]. These and few more issues are addressed in this paper. We have numerically tested our newly proposed scheme by solving several multi-phase flow settings such as an air bubble rising in water, a Rayleigh–Taylor instability problem that is initiated by placing a heavy fluid on top of a lighter one, and a droplet problem in which a water droplet hits the pool of water. Our numerical results show that we have achieved the second-order time accuracy without any order reductions. Moreover, the interfaces between the fluids are captured reasonably well.

Generative adversarial networks for dual-modality electrical tomography in multi-phase flow measurement

Measurement ◽  
2020 ◽  
pp. 108608
Author(s):  
Zihan Xia ◽  
Ziqiang Cui ◽  
Yuxiang Chen ◽  
Yafeng Hu ◽  
Huaxiang Wang
Keyword(s):  
Flow Measurement ◽  
Generative Adversarial Networks ◽  
Phase Flow ◽  
Electrical Tomography ◽  
Dual Modality ◽  
Adversarial Networks ◽  
Multi Phase Flow ◽  
Multi Phase

Evaluation of the impact of multi-phase flow on reservoir signatures in the Wolfcamp shale

2020 ◽  
Vol 76 ◽  
pp. 103187
Author(s):  
C.R. Clarkson ◽  
B. Yuan ◽  
Z. Zhang ◽  
F. Tabasinejad ◽  
H. Behmanesh ◽  
...  
Keyword(s):  
Phase Flow ◽  
Multi Phase Flow ◽  
Multi Phase ◽  
The Impact

scholarly journals Global existence of solutions for a multi-phase flow: A drop in a gas-tube

2016 ◽  
Vol 13 (02) ◽  
pp. 381-415
Author(s):  
Debora Amadori ◽  
Paolo Baiti ◽  
Andrea Corli ◽  
Edda Dal Santo
Keyword(s):  
Global Existence ◽  
Existence Of Solutions ◽  
Inviscid Fluid ◽  
Phase Flow ◽  
Lagrangian Coordinates ◽  
Large Initial Data ◽  
Initial Value ◽  
Global Existence Of Solutions ◽  
Multi Phase Flow ◽  
Multi Phase

In this paper we study the flow of an inviscid fluid composed by three different phases. The model is a simple hyperbolic system of three conservation laws, in Lagrangian coordinates, where the phase interfaces are stationary. Our main result concerns the global existence of weak entropic solutions to the initial-value problem for large initial data.

Effect of Fluid Type and Multi-Phase Flow on Sand Production in Oil and Gas Wells

2017 ◽  
Author(s):  
Haotian Wang ◽  
Deepen P. Gala ◽  
Mukul M. Sharma
Keyword(s):  
Oil And Gas ◽  
Phase Flow ◽  
Fluid Type ◽  
Sand Production ◽  
Gas Wells ◽  
Oil And Gas Wells ◽  
Multi Phase Flow ◽  
Multi Phase

JOINT NUMERICAL MICRO-SCALE SIMULATIONS OF MULTI-PHASE FLOW AND NMR RELAXATION BEHAVIOR IN POROUS MEDIA

2013 ◽  
Author(s):  
Oliver Mohnke ◽  
Norbert Klitzsch ◽  
Maik Stiebler
Keyword(s):  
Porous Media ◽  
Nmr Relaxation ◽  
Relaxation Behavior ◽  
Phase Flow ◽  
Micro Scale ◽  
Multi Phase Flow ◽  
Multi Phase
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