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Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations -
Chun-fang Shen, M. Sun (2015)
Instability of Riemann solutions to a scalar conservation law with discontinuous fluxZeitschrift für angewandte Mathematik und Physik, 66
- Publisher
- Springer Journals
- Copyright
- Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2022
- ISSN
- 0026-9255
- eISSN
- 1436-5081
- DOI
- 10.1007/s00605-022-01688-z
- Publisher site
- See Article on Publisher Site
Abstract
The Riemann problem for the isentropic drift-flux equations of gas-liquid two-phase flows under the equation of state for Chaplygin gas is investigated in detail, whose Riemann solution consists of either a delta shock wave or the combination of three contact discontinuities depending on the choice of Riemann initial data. In the delta shock wave solution, the Dirac delta function is developed simultaneously in the two densities of gas and liquid. Moreover, the weights of Dirac delta functions for the two densities and the propagation speed of delta shock wave are calculated explicitly by using the generalized Rankine-Hugoniot conditions. Furthermore, the wave interaction problems are considered in some specially designated circumstances. Some interesting nonlinear phenomena can be observed and analyzed carefully during the process of wave interactions. For instance, the interaction between a delta shock wave and a contact discontinuity produces two contact discontinuities and one delta contact discontinuity as well as the interaction between contact discontinuities belonging to different families leads to a delta shock wave.
Journal
Monatshefte für Mathematik – Springer Journals
Published: Apr 1, 2022
Keywords: Riemann problem; Delta shock wave; Two-phase flow; Wave interaction; 35L65; 35L67; 76N15