Affordable, entropy-consistent Euler flux functions II: Entropy production at shocks

By Farzad Ismail, Philip L. Roe. Journal of Computational Physics, 2009

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Arbitrarily High-order Accurate Entropy Stable Essentially Nonoscillatory Schemes for Systems of Conservation Laws (2012, methodology): “In a recent paper [15], Ismail and Roe have constructed an explicit solution of (2.”
Kinetic energy preserving and entropy stable finite volume schemes for compressible Euler and Navier-Stokes equations (2012, methodology): “If β= (1)6 then the entropy production across a weak shock due to matrix dissipation corresponds to the correct entropy production of O(∆ρ)3 as shown in [10].”
Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces (2014, methodology): “The study provides evidence that the nondissipative Euler fluxes of Ismail and Roe [24] do not degrade the formal accuracy.”
High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains (2013, methodology): “The study provides evidence that the the non-dissipative Euler fluxes of Ismail and Roe [8] do not degrade the formal accuracy of the high-order entropy consistent fluxes.”