  Non-ideal state equations are needed to compute a growing number of
engineering-relevant problems. The additional computational overhead from the
complex thermodynamics accounts for a significant portion of the total
computation, especially the near-critical or transcritical thermodynamic
regimes. A compromise between computational speed and the accuracy of the
thermodynamic property evaluations results in a propagation of the error from
the thermodynamics to the hydrodynamic computations. This work proposes a
systematic error quantification and computational cost estimate of the various
approaches for equation of state computation for use in compressible
Navier-Stokes solvers in the supercritical regime. We develop a parallelized,
high-order, finite volume solver with highly-modular thermodynamic
implementation to compute the compressible equations in conservative form.
Three tabular approaches are investigated: homogeneous tabulation, block
structured adaptive mesh refinement tabulation, and a n-dimensional Bezier
surface patch on an adaptive structured mesh. We define a set of standardized
error metrics and evaluate the thermodynamic error, table size and
computational expense for each approach. We also present an uncertainty
quantification methodology for tabular equation of state.
