On the well-posedness of the multi-dimensional Roe-Liu-Vinokur linearization for residual distribution schemes

In reference, Liu and Vinokur proposed an strategy to derive a Roe-like linearization for flows in thermo-chemical non-equilibrium (TCNEQ). In the context of approximated Riemann solvers, being able to determine a Roe-like averaged state Z→avg respecting property U guarantees that a discrete linearized description of the Riemann problem provides a solution consistent with that of the original non-linear problem, i.e., the numerical algorithm can - in the words of Roe - "recognize a shock wave"