Premium
Calculation of vertical velocity in three‐dimensional, shallow water equation, finite element models
Author(s) -
Muccino J. C.,
Gray W. G.,
Foreman M. G. G.
Publication year - 1997
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/(sici)1097-0363(19971015)25:7<779::aid-fld586>3.0.co;2-f
Subject(s) - mathematics , overdetermined system , boundary value problem , finite element method , mathematical analysis , computation , adjoint equation , boundary (topology) , geometry , partial differential equation , physics , algorithm , thermodynamics
Computation of vertical velocity within the confines of a three‐dimensional, finite element model is a difficult but important task. This paper examines four approaches to the solution of the overdetermined system of equations arising when the first‐order continuity equation is solved in conjunction with two boundary conditions. The traditional (TRAD) method neglects one boundary condition, solving the continuity equation with the remaining boundary condition. The vertical derivative of continuity (VDC) method involves solution of the second‐order equation obtained by differentiation of the continuity equation with respect to the vertical co‐ordinate. The least squares (LS) method minimizes the residuals of the continuity equation (in discrete form) and the two boundary conditions. The adjoint (ADJ) method minimizes the residuals of the continuity equation (in continuous form) and the two boundary conditions. Two domains are considered: a quarter‐annular harbour and the southwest coast of Vancouver Island. Results indicate that the highest‐quality solution is obtained with both LS and ADJ. Furthermore, ADJ requires less CPU and memory than LS. Therefore the optimal method for computation of vertical velocity in a three‐dimensional finite element model is the adjoint (ADJ) method. © 1997 John Wiley & Sons, Ltd.