Affiliation:
1. Department of Mathematics , Yunnan University , Kunming , Yunnan 650091 , P. R. China
Abstract
Abstract
This paper is concerned with the pressureless gas dynamics with a space-dependent gravity or a time-dependent friction in two dimensions. The basic Riemann problems with two pieces of constant initial data are considered. By the characteristic analysis, the Riemann problems are constructively solved by two kinds of solutions: vacuum solution and delta-shock solution, which describe the phenomena of cavitation and concentration, respectively. Especially, the generalized Rankine–Hugoniot relations for delta-shock waves are clarified and applied to the Riemann problems.
Funder
National Natural Science Foundation of China
Subject
Physical and Theoretical Chemistry,General Physics and Astronomy,Mathematical Physics
Reference33 articles.
1. Y. Li and Y. Cao, “Second order large particle difference method,” Sci. China, vol. 8, pp. 1024–1035, 1985.
2. S. Shandarin and Y. Zeldovich, “The large-scale structure of the universe: turbulence, intermittency, structure in a self-gravitating medium,” Rev. Mod. Phys., vol. 61, pp. 185–220, 1989. https://doi.org/10.1103/revmodphys.61.185.
3. L. Kofman, D. Pogosyan, and S. Shandarin, “Structure of the universe in the two-dimensional model of adhesion,” Mon. Nat. R. Astr. Soc., vol. 242, pp. 200–208, 1990. https://doi.org/10.1093/mnras/242.2.200.
4. R. Agarwal and D. Halt, “A modified CUSP scheme in wave/particle split for unstructured grid Euler flow,” in Frontiers of Computational Fluid Dynamics, New York, Wiley, 1994, pp. 155–163.
5. F. Bouchut, “On zero pressure gas dynamics,” in Advances in Kinetic Theory and Computing: Selected Papers, Series on Advances in Mathematics for Applied Sciences: Volume 22, River Edge, NJ, World Scientific, 1994, pp. 171–190.