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

• Published in: Journal of computational physics Vol. 378; pp. 760 - 769
• Main Authors: Garicano-Mena, Jesús, Degrez, Gérard
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 01.02.2019; Elsevier Science Ltd
• Subjects: Aerodynamics; Computational fluid dynamics; Computational physics; Fluid dynamics; Hypersonic flow; Linearization; Numerical analysis; Organic chemistry; Residual distribution schemes; Riemann solver; Roe linearization; Shock waves; Solvers; Thermo-chemical non-equilibrium; Thermodynamic models; Thermodynamics; Unstructured grids; Well posed problems; Residual distribution schemes; Hypersonic flow; Unstructured grids; Thermo-chemical non-equilibrium; Computational fluid dynamics; Roe linearization
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2018.11.007

In reference, Liu and Vinokur proposed an strategy to derive a Roe-like linearization for flows in thermo-chemical non-equilibrium. In the context of approximated Riemann solvers, being able to determine a Roe-like averaged state Zavg 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". Liu and Vinokur's accomplishment was to offer Roe-like averaged states Zavg under conditions for which the existence of such averages was not guaranteed, namely for complex, highly non-linear thermodynamic models. References illustrate the usage of Liu and Vinokur's generalized Roe average for combustion applications.