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A note on the flow equations under space‐time transformation
Author(s) -
Wu Z.N.
Publication year - 2004
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.200310133
Subject(s) - inviscid flow , transformation (genetics) , compressibility , flow (mathematics) , mathematics , space (punctuation) , spacetime , mathematical analysis , compressible flow , incompressible flow , space time , type (biology) , physics , classical mechanics , geometry , mechanics , geology , computer science , paleontology , biochemistry , chemistry , quantum mechanics , chemical engineering , engineering , gene , operating system
The equations governing incompressible and compressible inviscid flows and written in the physical frame ( t , x , y , z ) are known to be linearly well‐posed and exhibit elliptic or hyperbolic nature. The linear well‐posedness is considered here for these equations under a space‐time transformation ( t , x , y , z ) → (τ,ξ,η,ς), where the pseudo‐time τ and the new space coordinate (ξ,η,ς) all depend on ( t , x , y , z ). This type of transformation is typical in Computational Fluid Dynamics when local time‐stepping is used and it could be useful for uniformly treating problems such as mixed fast‐slow unsteady flows in which the flow is fast unsteady somewhere and slowly unsteady or steady elsewhere and mixed incompressible‐compressible flows. It is found that the transformation may alter the ellipticity, the hyperbolicity, and even the well‐posedness of the original equations.