A method is described for modifying the velocity field in geophysical fluid models so as to enforce the continuity equation. A corrective mass flux is introduced, which derives from a scalar potential. The latter is the solution of a Poisson problem which is formulated in such a way that a suitable norm of the corrective velocity be minimum. It is seen that a generalised vertical coordinate may be used. Finally, an elementary, one-dimensional illustration of the functioning of the method suggested is provided. (C) 2001 Elsevier Science Ltd. All rights reserved.
Deleersnijder, E. (2001). Enforcing the continuity equation in numerical models of geophysical fluid flows. Applied Mathematics Letters, 14(7), 867-873. https://doi.org/10.1016/S0893-9659(01)00057-X (Original work published 2001)