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Non-ideal state equations are needed to compute a growing number ofengineering-relevant problems. The additional computational overhead from thecomplex thermodynamics accounts for a significant portion of the totalcomputation, especially the near-critical or transcritical thermodynamicregimes. A compromise between computational speed and the accuracy of thethermodynamic property evaluations results in a propagation of the error fromthe thermodynamics to the hydrodynamic computations. This work proposes asystematic error quantification and computational cost estimate of the variousapproaches for equation of state computation for use in compressibleNavier-Stokes solvers in the supercritical regime. We develop a parallelized,high-order, finite volume solver with highly-modular thermodynamicimplementation to compute the compressible equations in conservative form.Three tabular approaches are investigated: homogeneous tabulation, blockstructured adaptive mesh refinement tabulation, and a n-dimensional Beziersurface patch on an adaptive structured mesh. We define a set of standardizederror metrics and evaluate the thermodynamic error, table size andcomputational expense for each approach. We also present an uncertaintyquantification methodology for tabular equation of state.

Uncertainty quantification of tabulated supercritical thermodynamics for compressible Navier-Stokes solvers