  The implementation of the ellipsoidal statistical Bhatnagar-Gross-Krook
(ESBGK) method in the open-source particle code PICLas is extended for
multi-species modeling of polyatomic molecules, including internal energies
with multiple vibrational degrees of freedom. For this, the models of Mathiaud,
Mieussens, Pfeiffer, and Brull are combined. In order to determine the
transport coefficients of the gas mixture, Wilke's mixing rules and collision
integrals are compared. The implementation is verified with simulation test
cases of a supersonic Couette flow as well as a hypersonic flow around a
70{\deg} blunted cone. The solutions of the ESBGK method are compared to the
Direct Simulation Monte Carlo (DSMC) method to assess the accuracy, where
overall good agreement is achieved. In general, collision integrals should be
preferred for the determination of the transport coefficients, since the
results using Wilke's mixing rules show larger deviations in particular for
large mass ratios. Considering the computational efficiency of the methods, a
considerable reduction in computational time is possible with the ESBGK model.
