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The application of the method of characteristics for the simulation of nearly horizontal flow in two and three spatial dimensions
Author(s) -
Matsoukis P. F. C.
Publication year - 1992
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.1650140402
Subject(s) - hydrostatic equilibrium , flow (mathematics) , basis (linear algebra) , geology , mechanics , partial differential equation , mathematics , ekman number , geometry , mathematical analysis , physics , quantum mechanics
Abstract Certain free surface flows exhibit in nature negligible vertical accelerations and as a result the pressure within the fluid remains hydrostatic. The method of characteristics is developed as a solution technique for the integration of the partial differential equations describing this kind of flow. The equations are integrated over the depth to provide a two‐dimensional model which is then tested and validated by comparing its results with tide‐induced flows occurring in a number of cases where either analytical or observational data are available for comparison. On the basis of the results of the 2D model, a finite difference 3D model is developed which provides the values of the unknown velocities u , v and w along the three axes x , y and z . This combined 2D–3D model is verified by applying it in cases of wind‐induced flow inside closed or open basins for which the classical Ekman solution may be used as a testing means.