期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 248, 期 -, 页码 47-86出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2013.04.005
关键词
Phase-field model; Van der Waals fluid; Phase transition; Non-convex flux; Hyperbolic-elliptic mixed problem; Nonlinear stability; Entropy variables; Time integration; Isogeometric analysis
资金
- Office of Naval Research [N00014-08-1-0992]
- National Initiative for Modeling and Simulation (NIMS) fellowship
- J. Tinsley Oden Faculty Fellowship Research Program at the Institute for Computational Engineering and Sciences
- Research Programs of Xunta de Galicia
- European Research Council through the FP7 Ideas Starting Grant program [307201]
We propose a new methodology for the numerical solution of the isothermal Navier-Stokes-Korteweg equations. Our methodology is based on a semi-discrete Galerkin method invoking functional entropy variables, a generalization of classical entropy variables, and a new time integration scheme. We show that the resulting fully discrete scheme is unconditionally stable-in-energy, second-order time-accurate, and mass-conservative. We utilize isogeometric analysis for spatial discretization and verify the aforementioned properties by adopting the method of manufactured solutions and comparing coarse mesh solutions with overkill solutions. Various problems are simulated to show the capability of the method. Our methodology provides a means of constructing unconditionally stable numerical schemes for nonlinear non-convex hyperbolic systems of conservation laws. (c) 2013 Elsevier Inc. All rights reserved.
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