A generalized Riemann problem for quasi-one-dimensional gas flows |
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Authors: | James Glimm Guillermo Marshall Bradley Plohr |
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Institution: | 1. Department of Mathematics, The Rockefeller University, New York, New York, 10021 USA;2. Also at Courant Institute of Mathematical Sciences, New York University, New York, N.Y. 10012 USA |
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Abstract: | A generalization of the Riemann problem for gas dynamical flows influenced by curved geometry, such as flows in a variable-area duct, is solved. For this generalized Riemann problem the initial data consist of a pair of steady-state solutions separated by a jump discontinuity. The solution of the generalized Riemann problem is used as a basis for a random choice method in which steady-state solutions are used as an Ansatz to approximate the spatial variation of the solution between grid points. For nearly steady flow in a Laval nozzle, where this Ansatz is appropriate, this generalized random choice method gives greatly improved results. |
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