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

Abstract

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.