  Numerical simulations of compressible fluid flows require an equation of
state (EOS) to relate the thermodynamic variables of density, internal energy,
temperature, and pressure. A valid EOS must satisfy the thermodynamic
conditions of consistency (derivation from a free energy) and stability
(positive sound speed squared). When phase transitions are significant, the EOS
is complicated and can only be specified in a table. For tabular EOS's such as
SESAME from Los Alamos National Laboratory, the consistency and stability
conditions take the form of a differential equation relating the derivatives of
pressure and energy as functions of temperature and density, along with
positivity constraints. Typical software interfaces to such tables based on
polynomial or rational interpolants compute derivatives of pressure and energy
and may enforce the stability conditions, but do not enforce the consistency
condition and its derivatives. We describe a new type of table interface based
on a constrained local least squares regression technique. It is applied to
several SESAME EOS's showing how the consistency condition can be satisfied to
round-off while computing first and second derivatives with demonstrated
second-order convergence. An improvement of 14 orders of magnitude over
conventional derivatives is demonstrated, although the new method is apparently
two orders of magnitude slower, due to the fact that every evaluation requires
solving an 11-dimensional nonlinear system.
