The Riemann problem for the Eulerian droplet model with buoyancy and gravity forces
College of Mathematics and Statistics, Xinyang Normal University, Xinyang, 464000, People’s Republic of China
2 Department of Mathematics, Yunnan Normal University, Kunming, 650500, People’s Republic of China
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Accepted: 21 November 2019
Published online: 1 February 2020
Under the premise of considering buoyancy and gravity forces, this paper makes a more detailed study on the one-dimensional Eulerian droplet model from a theoretical aspect focusing on exploring its Riemann problem. This model can be considered the pressureless Euler system with two external forces. The Riemann solutions are constructively obtained. They involve delta-shock solution and vacuum solution. Using generalized Rankine–Hugoniot relation, we derive in greater detail the position, propagation speed and strength of delta-shock wave under a suitable entropy condition. Furthermore, we investigate the limit behaviors of the Riemann solutions when external forces vanish partially or completely.
© Società Italiana di Fisica (SIF) and Springer-Verlag GmbH Germany, part of Springer Nature, 2020