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| Multidimensional simple wave andMonge-Amp`ere equation: theoryand applications |
| Boling Guo,Yueyang Feng,Yaqing Liu |
| (Institute of Applied Physics and Computational Mathematics, Beijing,
100088, China;The Graduate School of China Academy of Engineering Physics, Beijing,
100088, China;School of Applied Science, Beijing Information Science and Technology
University, Beijing 100192, China) |
| DOI： |
| Abstract: |
| This paper explores the properties and mathematical formulations
of multidimensional simple waves, extending the well-established theory of onedimensional simple waves to higher dimensions. The study focuses on the connection between simple waves and the Monge-Amp`ere equation, particularly
in the context of gas dynamics and potential flows. Key aspects include the
characterization of simple waves in unsteady and steady flows, the role of characteristic lines, and the application of Hodograph and Legendre transformations
to derive solutions. The paper also addresses the challenges and open questions
in extending simple wave theory to more complex systems, such as non-reducible
systems, radiative heat transfer, and chemical reactions. The research highlights
both theoretical advancements and practical applications, providing a foundation for future studies in this area. |
| Key words: Simple wave; Monge-Amp`ere equation; Gas dynamics; Characteristic lines;
Hodograph transformation. |