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Exact and approximate boundary conditions at artificial boundaries
Author(s) -
Lill Georg
Publication year - 1993
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.1670161003
Subject(s) - mathematics , mathematical analysis , boundary value problem , scalar (mathematics) , compressibility , boundary (topology) , transformation (genetics) , hyperbolic partial differential equation , partial differential equation , geometry , mechanics , physics , biochemistry , chemistry , gene
The use of transformation methods for the derivation of boundary conditions at artificial boundaries had been initiated by Engquist and Majda [4. 5]. They considered the scalar wave equation and strictly hyperbolic systems. This has been extended by Gustafsson [11] to inhomogeneous conditions, by Hagstrom [15] to parabolic and Halpern et al . [17, 20] to incompletely parabolic systems. Here a systematic method is developed which unifies these approaches. Additionally, inhomogeneities with non‐compact support are taken into account. Exact and first‐order approximate boundary conditions for the compressible Navier–Stokes equations are presented.