Comparisons between exact and tabulated approaches for the partially hydrogen gas EoS. The black dashed line corresponds to computations obtained with the iterative root-finder approach outlined in Sect. 3.2.1 while the red and green solid lines corresponds to the tabulated approach presented in Sect. 3.2.2. Left: gas internal energy (Eq. (B.1)) around the transition region. Middle: fundamental gas derivative (Eq. (A.1)) computed using standard central differencing. The large spikes in the red curve are due to discontinuous first derivatives using linear interpolation between adjacent node values in the table. Right: density profile in the Sod shock tube at t = 0.2 using the exact and spline approaches. It is clear the appearance of spurious compound structures in the rarefaction wave when a linear spline is used to approximate the table.