Isogeometric analysis of the isothermal Navier–Stokes–Korteweg equations

• DOI: 10.1016/j.cma.2010.02.010
• Publication Date: 2010-03-08T07:38:57Z
• Authors: Hector Gomez; Thomas J.R. Hughes; Xesús Nogueira; Victor M. Calo
• Keywords: Isogeometric analysis; Vaporization; Condensation; 0211 other engineering and technologies; Phase-field; 02 engineering and technology; Navier-Stokes-Korteweg

This paper is devoted to the numerical simulation of the Navier-Stokes-Korteweg equations, a phase-eld model for water/water-vapor two-phase ows. We develop a numerical formulation based on isogeometric analysis that permits straightforward treatment of the higher-order partial-dierenti al operator that represents capillarity. We introduce a new renement 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 eectiveness and robustness of our approach.