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Stability of the Numerical Solution of Transonic Potential Flow
Author(s) -
Maršík F.,
Danêk V.
Publication year - 1993
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19930730314
Subject(s) - dissipative system , viscosity , transonic , mechanics , dissipation , shock wave , flow (mathematics) , variational principle , stability (learning theory) , classical mechanics , mathematics , physics , thermodynamics , computer science , aerodynamics , machine learning
Abstract The influence of an artificial viscosity on the stability of numerical solution of transonic flows with shock waves is investigated. The variational principle with dissipation introduced through a physical viscosity is derived, and a simplified relation describing the stabilizing influence of the dissipative process is presented. The numerical solution of the potential equation by FEM is examined and compared with the formulation using the variational principle. The correspondence between physical viscosity μ and artificial viscosity μ num is shown both qualitatively and quantitatively. The necessary amount of artificial viscosity is investigated analytically and the results are compared with numerical experiments.