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Numerical solutions to the self‐similar transonic two‐dimensional nonlinear wave system
Author(s) -
Kim Eun Heui,
Lee ChungMin
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1350
Subject(s) - transonic , shock wave , shock (circulatory) , mathematics , riemann problem , riemann hypothesis , nonlinear system , mathematical analysis , numerical analysis , object (grammar) , physics , mechanics , computer science , aerodynamics , medicine , quantum mechanics , artificial intelligence
We present numerical results on a two‐dimensional Riemann problem governed by the self‐similar nonlinear wave system that gives rise to a transonic shock. We consider a configuration for a vertical incident shock moving to the right above a rectangular object. The incident shock then interacts with a sonic circle soon after it moves beyond the object, and creates a transonic region. We implement Lax–Liu positive schemes and Strang splitting, and obtain several numerical solutions for the model system. With the numerical results that we have obtained, we present several analyses of the transonic shock strengths and the positions of the transonic shocks with various Riemann data. Moreover, due to the presence of the corner of the object, numerical oscillations are apparent. We discuss regularity results for the solution near the corner of the object. Copyright © 2010 John Wiley & Sons, Ltd.