The Incompressible Unsteady Navier-Stokes Equations

The package ´SegregatedVMSSolver´ solves the unsteady incompressible Navier-Stokes. The conservation equations takes the following form:

Mass Conservation

$R_c = \nabla\cdot(u)=0$

Momentum Conservation

$R_m = \frac{\partial u}{\partial t} + u\cdot\nabla(u) +\nabla(p) -\nu \Delta(u) = f$

Where:

• $u$ is the velocity field
• $p$ is the pressure (normalized with density, assumed to be unitary)
• $\nu$ is the kinematic viscosity of the fluid
• $f$ is the momentum source term