Velocity/pressure coupling of the Navier-Stokes equations is solved thanks to a pressure correction method. The Goda method [1] is used for monophasic flows, whereas the Timmermans one [2] is used for multiphase flows. This choice is done automatically depending on the presence of the advection equation in the NTS file. Methods are written here.

Even if the Goda method can also be used for monophasic flows, it is less precise than the Timmermans method. One have to remind that the latter takes advantage of a constant viscosity to rewrite the stress term with the \(rot \times rot\) operator.

So, if the Notus user modifies the viscosity thanks to the user routine, the automatic choice may not be valid anymore, which means that the choice of the pressure correction method must be forced in the NTS file:

velocity_pressure_method incremental_pressure_correction; # [OPTIONAL], incremental_pressure_correction [1] or rotational_incremental_pressure_correction [2]

[1] K. Goda, A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows, Journal of Computational Physics 30 (1979) 76–95.

[2] L. J. P. Timmermans, P. D. Minev, F. N. Van De Voss, An approximate projection scheme for incompressible flow using spectral elements, International Journal for Numerical Methods in Fluids 22 (1996) 673–688.