Concentration and cavitation phenomena of Riemann solutions for the isentropic Euler system with the logarithmic equation of state. (June 2020)

• Record Type: Journal Article
• Authors: Sun, Meina
• Is Part Of: Nonlinear analysis. Volume 53(2020)
• Publication Date: 2020-06
• Subjects: Isentropic Euler system -- Logarithmic equation of state -- Delta shock wave -- Vacuum state -- Riemann problem; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.103068
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: The analytical solutions of the Riemann problem for the isentropic Euler system with the logarithmic equation of state are derived explicitly for all the five different cases. The concentration and cavitation phenomena are observed and analyzed during the process of vanishing pressure in the Riemann solutions. It is shown that the solution consisting of two shock waves converges to a delta shock wave solution as well as the solution consisting of two rarefaction waves converges to a solution consisting of four contact discontinuities together with vacuum states with three different virtual velocities in the limiting situation.