Fast evaluation of complex equations of state

Abstract

One of the most common operations encountered in computational fluid dynamics (CFD) solvers is the evaluation of the caloric and thermal equations of state (EoS) which are required to compute thermodynamic state variables from the conserved values that are typically being advanced by the simulation. The complexity of these calculations can vary widely depending on the nature of the fluid under consideration. We present a method for generating an interpolated representation of the EoS that is fairly inexpensive to evaluate regardless of the complexity of the actual underlying state equations. This approach has the advantage of being agnostic towards the original representation; whether it be a complex analytic expression, expensive iterative method, or interpolated from empirical data.

Keywords

• Tabular approximation
• adaptive sampling
• Bezier surface
• spline
• interpolation