Efficient numerical methods for simulating surface tension of multi-component mixtures with the gradient theory of fluid interfaces

Handle URI:
http://hdl.handle.net/10754/564196
Title:
Efficient numerical methods for simulating surface tension of multi-component mixtures with the gradient theory of fluid interfaces
Authors:
Kou, Jisheng; Sun, Shuyu ( 0000-0002-3078-864X ) ; Wang, Xiuhua
Abstract:
Surface tension significantly impacts subsurface flow and transport, and it is the main cause of capillary effect, a major immiscible two-phase flow mechanism for systems with a strong wettability preference. In this paper, we consider the numerical simulation of the surface tension of multi-component mixtures with the gradient theory of fluid interfaces. Major numerical challenges include that the system of the Euler-Lagrange equations is solved on the infinite interval and the coefficient matrix is not positive definite. We construct a linear transformation to reduce the Euler-Lagrange equations, and naturally introduce a path function, which is proven to be a monotonic function of the spatial coordinate variable. By using the linear transformation and the path function, we overcome the above difficulties and develop the efficient methods for calculating the interface and its interior compositions. Moreover, the computation of the surface tension is also simplified. The proposed methods do not need to solve the differential equation system, and they are easy to be implemented in practical applications. Numerical examples are tested to verify the efficiency of the proposed methods. © 2014 Elsevier B.V.
KAUST Department:
Computational Transport Phenomena Lab; Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program
Publisher:
Elsevier BV
Journal:
Computer Methods in Applied Mechanics and Engineering
Issue Date:
Aug-2015
DOI:
10.1016/j.cma.2014.10.023
Type:
Article
ISSN:
00457825
Sponsors:
This work is supported by National Natural Science Foundation of China (No. 11301163), the Key Project of Chinese Ministry of Education (No. 212109) and the KAUST faculty research fund (No. PID7000000058).
Appears in Collections:
Articles; Environmental Science and Engineering Program; Physical Sciences and Engineering (PSE) Division; Computational Transport Phenomena Lab

Full metadata record

DC FieldValue Language
dc.contributor.authorKou, Jishengen
dc.contributor.authorSun, Shuyuen
dc.contributor.authorWang, Xiuhuaen
dc.date.accessioned2015-08-03T12:36:02Zen
dc.date.available2015-08-03T12:36:02Zen
dc.date.issued2015-08en
dc.identifier.issn00457825en
dc.identifier.doi10.1016/j.cma.2014.10.023en
dc.identifier.urihttp://hdl.handle.net/10754/564196en
dc.description.abstractSurface tension significantly impacts subsurface flow and transport, and it is the main cause of capillary effect, a major immiscible two-phase flow mechanism for systems with a strong wettability preference. In this paper, we consider the numerical simulation of the surface tension of multi-component mixtures with the gradient theory of fluid interfaces. Major numerical challenges include that the system of the Euler-Lagrange equations is solved on the infinite interval and the coefficient matrix is not positive definite. We construct a linear transformation to reduce the Euler-Lagrange equations, and naturally introduce a path function, which is proven to be a monotonic function of the spatial coordinate variable. By using the linear transformation and the path function, we overcome the above difficulties and develop the efficient methods for calculating the interface and its interior compositions. Moreover, the computation of the surface tension is also simplified. The proposed methods do not need to solve the differential equation system, and they are easy to be implemented in practical applications. Numerical examples are tested to verify the efficiency of the proposed methods. © 2014 Elsevier B.V.en
dc.description.sponsorshipThis work is supported by National Natural Science Foundation of China (No. 11301163), the Key Project of Chinese Ministry of Education (No. 212109) and the KAUST faculty research fund (No. PID7000000058).en
dc.publisherElsevier BVen
dc.rights© 2015.This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subjectEuler-Lagrange equationsen
dc.subjectGradient theoryen
dc.subjectMulti-component mixturesen
dc.subjectSurface tensionen
dc.titleEfficient numerical methods for simulating surface tension of multi-component mixtures with the gradient theory of fluid interfacesen
dc.typeArticleen
dc.contributor.departmentComputational Transport Phenomena Laben
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.identifier.journalComputer Methods in Applied Mechanics and Engineeringen
dc.contributor.institutionHubei Engn Univ, Sch Math & Stat, Xiaogan 432000, Hubei, Peoples R Chinaen
dc.contributor.institutionXi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R Chinaen
kaust.authorSun, Shuyuen
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