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

In reference [1], 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 respecting property U (see [2]) 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”.