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

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.
Authors:
 [1] ;  [2] ; ;  [1] ;  [3]
  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)
Publication Date:
OSTI Identifier:
22230783
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 248; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
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