Summary
The method of strained coordinates is extended to expand the dependent variables as well as independent coordinates of a nonlinear hyperbolic system in asymptotic series of several parameters. The perturbation parameters may be of a different nature but are required to be intrinsically independent of each other. The method is found to be particularly useful for treating problems with several relevant parameters being of the same order of one another. The illustrative example discussed is a nonlinear supersonic nonequilibrium flow over a wedge where the nonlinear effect in the flow becomes of the same order as the nonequilibrium effect. A second-order theory is developed to provide a description of the near-field flow pattern and the expression of the front frozen shock wave attached to the nose of the wedge.
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Chou, D.C. On the multi-parameter characteristic perturbation method; Application to nonlinear supersonic nonequilibrium flow over a wedge. J Eng Math 6, 273–283 (1972). https://doi.org/10.1007/BF01535187
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DOI: https://doi.org/10.1007/BF01535187