Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations

Hector Gomez, Thomas Jr R Hughes, Xesús Nogueira, Victor M. Calo

Research output: Contribution to journalArticlepeer-review

180 Scopus citations


This paper is devoted to the numerical simulation of the Navier-Stokes-Korteweg equations, a phase-field model for water/water-vapor two-phase flows. We develop a numerical formulation based on isogeometric analysis that permits straightforward treatment of the higher-order partial-differential operator that represents capillarity. We introduce a new refinement methodology that desensitizes the numerical solution to the computational mesh and achieves mesh invariant solutions. Finally, we present several numerical examples in two and three dimensions that illustrate the effectiveness and robustness of our approach. © 2010 Elsevier B.V.
Original languageEnglish (US)
Pages (from-to)1828-1840
Number of pages13
JournalComputer Methods in Applied Mechanics and Engineering
Issue number25-28
StatePublished - May 2010

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: H. Gomez was partially supported by the J. Tinsley Oden Faculty Fellowship Research Program at the Institute for Computational Engineering and Sciences. H. Gomez and X. Nogueira gratefully acknowledge the funding provided by Xunta de Galicia (grants # 09REM005118PR and # 09MDS00718PR), Ministerio de Educacion y Ciencia (grants #DPI2007-61214 and #DPI2009-14546-C02-01) cofinanced with FEDER funds, and Universidade do Coruna. T.J.R. Hughes and V.M. Calo were partially supported by the Office of Naval Research under Contract Number N00014-08-1-0992. V.M. Calo was partially supported by a grant from King Abdullah University of Science and Technology under the KAUST-UT Austin Academic Excellence Agreement. We acknowledge the Texas Advanced Computing Center (TACC) and Teragrid, MCA075032, for the computational time.

ASJC Scopus subject areas

  • General Physics and Astronomy
  • Mechanics of Materials
  • Mechanical Engineering
  • Computational Mechanics
  • Computer Science Applications


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