Analysis of the Stability of the Riemann Problem for a Simplified Model in Magnetogasdynamics

The generalized Riemann problem for a simplified model of one-dimensional ideal gas in magnetogasdynamics in a neighborhood of the origin (t>0) in the (x,t) plane is considered. According to the different cases of the corresponding Riemann solutions, we construct the perturbed solutions uniquely...

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Bibliographic Details
Main Authors: Yujin Liu, Wenhua Sun
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2016/7526413
Description
Summary:The generalized Riemann problem for a simplified model of one-dimensional ideal gas in magnetogasdynamics in a neighborhood of the origin (t>0) in the (x,t) plane is considered. According to the different cases of the corresponding Riemann solutions, we construct the perturbed solutions uniquely with the characteristic method. We find that, for some case, the contact discontinuity appears after perturbation while there is no contact discontinuity of the corresponding Riemann solution. For most cases, the Riemann solutions are stable and the perturbation can not affect the corresponding Riemann solutions. While, for some few cases, the forward (backward) rarefaction wave can be transformed into the forward (backward) shock wave which shows that the Riemann solutions are unstable under such local small perturbations of the Riemann initial data.
ISSN:1687-9120
1687-9139