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A semi‐implicit method for vertical transport in multidimensional models
Author(s) -
Gross Edward S.,
Casulli Vincenzo,
Bonaventura Luca,
Koseff Jeffrey R.
Publication year - 1998
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(19980715)28:1<157::aid-fld144>3.0.co;2-u
Subject(s) - discretization , scalar (mathematics) , mathematics , range (aeronautics) , convection–diffusion equation , stability (learning theory) , von neumann architecture , mathematical optimization , computer science , mathematical analysis , geometry , engineering , machine learning , aerospace engineering , pure mathematics
A one‐dimensional scalar transport method which is appropriate for simulations over a wide range of Courant number is described. Von Neumann stability and matrix invertibility are guaranteed for all Courant numbers and the method has less diffusive and dispersive error than simpler implicit methods. It is implemented for vertical scalar transport in a three‐dimensional hydrodynamic model, with horizontal transport discretized explicitly. The method is applied and compared with simpler semi‐implicit methods in several test cases and used for a simulation of scalar transport in an estuary. © 1998 John Wiley & Sons, Ltd.