Functional entropy variables: A new methodology for deriving thermodynamically consistent algorithms for complex fluids, with particular reference to the isothermal Navier–Stokes–Korteweg equations

Journal Article · Sun Sep 01 04:00:00 EDT 2013 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2013.04.005· OSTI ID:22230783

Liu, Ju ^[1]; Gomez, Hector ^[2]; Evans, John A.; Hughes, Thomas J.R. ^[1]; Landis, Chad M. ^[3]

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1. Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th Street, 1 University Station C0200, Austin, TX 78712 (United States)
2. Department of Mathematical Methods, University of A Coruña, Campus de Elviña, s/n, 15192 A Coruña (Spain)
3. Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, 210 East 24th Street, 1 University Station C0600, Austin, TX 78712 (United States)

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.

• OSTI ID: 22230783
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 248; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
COMPARATIVE EVALUATIONS
CONSERVATION LAWS
ENTROPY
EQUATIONS
FLUIDS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PHASE TRANSFORMATIONS
SIMULATION
STABILITY
VAN DER WAALS FORCES