FDPDEType: FDPDE_STOKES

Stokes equations

The Stokes equations representing conservation of mass and momentum for single-phase flow are written in general form as

where $P$ pressure and $\textbf{u}$ velocity are the unknowns. The coefficients $A, B, C$ need to be defined by the user and are written here in a generic way in order to represent the whole spectrum of Stokes problems (i.e., compressible/incompressible, Newtonian/non-Newtonian rheology).

They briefly represent: $A$ - effective viscosity, $B$ - right-hand side for the momentum equation (i.e., body forces), $C$ - right-hand side for the continuity equation (i.e., incompressibility). These are elliptical equations and should be straight forward to solve.

The FDPDE_STOKES coefficients and unknowns are located on the staggered grid in the following way

where:

• A is a scalar field but located in both centers A_center (dof=1) and corners A_corner (dof=0),
• B is vector field located on faces, B = [Bx (dof=0), Bz (dof=0)],
• C is scalar field located in centers (dof=0).

See Tests for examples with FDPDE_STOKES

Back to User guide
Back to HOME