Consistent properties reconstruction on adaptive Cartesian meshes for complex fluids computations

  • Authors:

  • Guoping Xia;Ding Li;Charles L. Merkle

  • Affiliations:

  • Purdue University, West Lafayette, IN 47907, USA;Purdue University, West Lafayette, IN 47907, USA;Purdue University, West Lafayette, IN 47907, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2007

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Abstract

An efficient reconstruction procedure for evaluating the constitutive properties of a complex fluid from general or specialized thermodynamic databases is presented. Properties and their pertinent derivatives are evaluated by means of an adaptive Cartesian mesh in the thermodynamic plane that provides user-specified accuracy over any selected domain. The Cartesian grid produces a binary tree data structure whose search efficiency is competitive with that for an equally spaced table or with simple equations of state such as a perfect gas. Reconstruction is accomplished on a triangular subdivision of the 2D Cartesian mesh that ensures function continuity across cell boundaries in equally and unequally spaced portions of the table to C^0, C^1 or C^2 levels. The C^0 and C^1 reconstructions fit the equation of state and enthalpy relations separately, while the C^2 reconstruction fits the Helmholtz or Gibbs function enabling EOS/enthalpy consistency also. All three reconstruction levels appear effective for CFD solutions obtained to date. The efficiency of the method is demonstrated through storage and data retrieval examples for air, water and carbon dioxide. The time required for property evaluations is approximately two orders of magnitude faster with the reconstruction procedure than with the complete thermodynamic equations resulting in estimated 3D CFD savings of from 30 to 60. Storage requirements are modest for today's computers, with the C^1 method requiring slightly less storage than those for the C^0 and C^2 reconstructions when the same accuracy is specified. Sample fluid dynamic calculations based upon the procedure show that the C^1 and C^2 methods are approximately a factor of two slower than the C^0 method but that the reconstruction procedure enables arbitrary fluid CFD calculations that are as efficient as those for a perfect gas or an incompressible fluid for all three accuracy levels.