Eulerian droplet model: Delta-shock waves and solution of the Riemann\n problem

2017/10/18 by Sana Keita, Keita, Sana, Yves Bourgault +1 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1710.06904

openalex publication_date 2017/10/18 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We study an Eulerian droplet model which can be seen as the pressureless gas\nsystem with a source term, a subsystem of this model and the inviscid Burgers\nequation with source term. The condition for loss of regularity of a solution\nto Burgers equation with source term is established. The same condition applies\nto the Eulerian droplet model and its subsystem. The Riemann problem for the\nEulerian droplet model is constructively solved by going through the solution\nof the Riemann problems for the inviscid Burgers equation with a source term\nand the subsystem, respectively. Under suitable generalized Rankine-Hugoniot\nrelations and entropy condition, the existence of delta-shock solution is\nestablished. The existence of a solution to the generalized Rankine-Hugoniot\nconditions is proven. Some numerical illustrations are presented.\n

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