Adaptive and consistent properties reconstruction for complex fluids computation

Abstract

An efficient reconstruction procedure on adaptive Cartesian mesh for evaluating the constitutive properties of a complex fluid from general or specialized thermodynamic databases is presented. Reconstruction is accomplished on a triangular subdivision of the 2D Cartesian mesh covering thermodynamic plane of interest that ensures function continuity across cell boundaries 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. The time required for evaluations is approximately two orders of magnitude faster with the reconstruction procedure than with the complete thermodynamic equations. 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. © 2011 Springer-Verlag Berlin Heidelberg.