Abstract
In order to use the second-order 5-point difference scheme mentioned to compute the solution of one dimension unsteady equations of the direct reflection of the strong plane detonation wave meeting a solid wall barrier, in this paper, we technically construct the difference schemes of the boundary and sub-boundary of the problem, and deduce the auto-analogue analytic solutions of the initial value problem, and at the same time, we present a method for the singular property of the initial value problem, from which we can get a satisfactory computation result of this difficult problem.
The difference scheme used in this paper to deal with the discontinuity problems of the shock wave are valuable and worth generalization.
Similar content being viewed by others
References
Harten, A.,High Resolution Schemes for Hyperbolic Conservation, Laus (1983).
Huang Dun, A series of analytical solutions of higher order accuracy for air-dynamics coupled equations,Yearly Thesis for Mathematics of Computation (1979). (in Chinese)
Wu Xiong-hua, The application of singularity-separation method to the computation of unsteady shock,Mathematics of Computation and Computer Applications,3, 3 (1982). (in Chinese)
Zhon Ning, Reflection of unsteady blast wave computed by second order accurate MUDVL scheme,Journal of Computational Physics Sinica,1, 1 (1984), 21–30. (in Chinese)
Author information
Authors and Affiliations
Additional information
Communicated by Pan Li-zhou
Rights and permissions
About this article
Cite this article
Shao-jun, C. Harten solution for one-dimensional unsteady equation. Appl Math Mech 14, 545–554 (1993). https://doi.org/10.1007/BF02451363
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02451363