Two-phase incompressible flows with variable density

An energetic variational approach

Jie Jiang, Yinghua Li, Chun Liu

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper, we study a diffuse-interface model for two-phase incompressible flows with different densities. First, we present a derivation of the model using an energetic variational approach. Our model allows large density ratio between the two phases and moreover, it is thermodynamically consistent and admits a dissipative energy law. Under suitable assumptions on the average density function, we establish the global existence of a weak solution in the 3D case as well as the global well-posedness of strong solutions in the 2D case to an initial-boundary problem for the resulting Allen-Cahn-Navier-Stokes system. Furthermore, we investigate the longtime behavior of the 2D strong solutions. In particular, we obtain existence of a maximal compact attractor and prove that the solution will converge to an equilibrium as time goes to infinity.

Original language English (US) 3243-3284 42 Discrete and Continuous Dynamical Systems- Series A 37 6 https://doi.org/10.3934/dcds.2017138 Published - Jan 1 2017

Fingerprint

Incompressible flow
Variational Approach
Two-phase Flow
Incompressible Flow
Strong Solution
Diffuse Interface
Global Well-posedness
Navier-Stokes System
Long-time Behavior
Boundary Problem
Density Function
Global Existence
Probability density function
Weak Solution
Attractor
Infinity
Model
Converge
Energy

All Science Journal Classification (ASJC) codes

• Analysis
• Discrete Mathematics and Combinatorics
• Applied Mathematics

Cite this

title = "Two-phase incompressible flows with variable density: An energetic variational approach",
abstract = "In this paper, we study a diffuse-interface model for two-phase incompressible flows with different densities. First, we present a derivation of the model using an energetic variational approach. Our model allows large density ratio between the two phases and moreover, it is thermodynamically consistent and admits a dissipative energy law. Under suitable assumptions on the average density function, we establish the global existence of a weak solution in the 3D case as well as the global well-posedness of strong solutions in the 2D case to an initial-boundary problem for the resulting Allen-Cahn-Navier-Stokes system. Furthermore, we investigate the longtime behavior of the 2D strong solutions. In particular, we obtain existence of a maximal compact attractor and prove that the solution will converge to an equilibrium as time goes to infinity.",
author = "Jie Jiang and Yinghua Li and Chun Liu",
year = "2017",
month = "1",
day = "1",
doi = "10.3934/dcds.2017138",
language = "English (US)",
volume = "37",
pages = "3243--3284",
journal = "Discrete and Continuous Dynamical Systems",
issn = "1078-0947",
publisher = "Southwest Missouri State University",
number = "6",

}

Two-phase incompressible flows with variable density : An energetic variational approach. / Jiang, Jie; Li, Yinghua; Liu, Chun.

In: Discrete and Continuous Dynamical Systems- Series A, Vol. 37, No. 6, 01.01.2017, p. 3243-3284.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Two-phase incompressible flows with variable density

T2 - An energetic variational approach

AU - Jiang, Jie

AU - Li, Yinghua

AU - Liu, Chun

PY - 2017/1/1

Y1 - 2017/1/1

N2 - In this paper, we study a diffuse-interface model for two-phase incompressible flows with different densities. First, we present a derivation of the model using an energetic variational approach. Our model allows large density ratio between the two phases and moreover, it is thermodynamically consistent and admits a dissipative energy law. Under suitable assumptions on the average density function, we establish the global existence of a weak solution in the 3D case as well as the global well-posedness of strong solutions in the 2D case to an initial-boundary problem for the resulting Allen-Cahn-Navier-Stokes system. Furthermore, we investigate the longtime behavior of the 2D strong solutions. In particular, we obtain existence of a maximal compact attractor and prove that the solution will converge to an equilibrium as time goes to infinity.

AB - In this paper, we study a diffuse-interface model for two-phase incompressible flows with different densities. First, we present a derivation of the model using an energetic variational approach. Our model allows large density ratio between the two phases and moreover, it is thermodynamically consistent and admits a dissipative energy law. Under suitable assumptions on the average density function, we establish the global existence of a weak solution in the 3D case as well as the global well-posedness of strong solutions in the 2D case to an initial-boundary problem for the resulting Allen-Cahn-Navier-Stokes system. Furthermore, we investigate the longtime behavior of the 2D strong solutions. In particular, we obtain existence of a maximal compact attractor and prove that the solution will converge to an equilibrium as time goes to infinity.

UR - http://www.scopus.com/inward/record.url?scp=85017548129&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85017548129&partnerID=8YFLogxK

U2 - 10.3934/dcds.2017138

DO - 10.3934/dcds.2017138

M3 - Article

VL - 37

SP - 3243

EP - 3284

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

SN - 1078-0947

IS - 6

ER -
{"ft_lang_label":"__label__en","ft_lang_prob":0.83466035,"math_prob":0.8978391,"size":3771,"snap":"2019-43-2019-47","text_gpt3_token_len":909,"char_repetition_ratio":0.09769047,"word_repetition_ratio":0.69588554,"special_character_ratio":0.23017767,"punctuation_ratio":0.10977443,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95238894,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-15T20:35:35Z\",\"WARC-Record-ID\":\"<urn:uuid:b98f0383-2112-4694-8ab6-6ddae258454b>\",\"Content-Length\":\"44065\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:12a81a02-28bb-4498-ad26-8620025bb066>\",\"WARC-Concurrent-To\":\"<urn:uuid:f92aec85-9686-4c2a-9def-22a56698aa60>\",\"WARC-IP-Address\":\"52.72.50.98\",\"WARC-Target-URI\":\"https://pennstate.pure.elsevier.com/en/publications/two-phase-incompressible-flows-with-variable-density-an-energetic\",\"WARC-Payload-Digest\":\"sha1:VRQ7MUKFSGENQA4PMNQBTPCWS6J7CHP5\",\"WARC-Block-Digest\":\"sha1:5LIB76NKBADGXPHWO3TRB6HZDAGMUVZW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986660231.30_warc_CC-MAIN-20191015182235-20191015205735-00321.warc.gz\"}"}