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Analysis of two‐dimensional, finite amplitude wave propagation by time marching methods
Author(s) -
Parker R.,
James M. N.
Publication year - 1982
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650020206
Subject(s) - inviscid flow , inflow , mathematics , perturbation (astronomy) , boundary (topology) , mathematical analysis , outflow , finite difference , boundary value problem , finite difference method , amplitude , fourier transform , finite volume method , mechanics , physics , meteorology , quantum mechanics
Two‐dimensional, finite‐amplitude wave propagation in an inviscid, subsonic, perfect gas medium is analysed by explicit finite‐difference methods. A two‐step, Lax‐Wendroff method and the single‐step, Lax‐Friedrichs method are used. A prescribed propagating velocity or pressure disturbance is applied along a single row of grid points normal to the stream direction and results in a 'forced' outflow boundary. The inflow boundary is placed far from outflow by utilizing a streamwise expanding grid and uniform inflow is imposed. Side boundaries are spatially periodic. The numerical solutions are compared with analytical small‐perturbation solutions; higher‐order effects arising from non‐linearities are revealed by Fourier analysis. Solutions which closely approached a periodic state were obtained. The Lax‐Wendroff method combined with the expanding grid is shown to be accurate and stable, the Lax‐Friedrichs scheme produced highly damped solutions.