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Consistency with continuity in conservative advection schemes for free‐surface models
Author(s) -
Gross Edward S.,
Bonaventura Luca,
Rosatti Giorgio
Publication year - 2002
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.222
Subject(s) - discretization , advection , mathematics , consistency (knowledge bases) , convection–diffusion equation , scalar (mathematics) , mathematical analysis , geometry , physics , thermodynamics
The consistency of the discretization of the scalar advection equation with the discretization of the continuity equation is studied for conservative advection schemes coupled to three‐dimensional flows with a free‐surface. Consistency between the discretized free‐surface equation and the discretized scalar transport equation is shown to be necessary for preservation of constants. In addition, this property is shown to hold for a general formulation of conservative schemes. A discrete maximum principle is proven for consistent upwind schemes. Various numerical examples in idealized and realistic test cases demonstrate the practical importance of the consistency with the discretization of the continuity equation. Copyright © 2002 John Wiley & Sons, Ltd.