# ALGORITHMS FOR INCOMPRESSIBLE FLOWS

# ALGORITHMS FOR INCOMPRESSIBLE FLOWS

This chapter presents different ways of formulating the incompressible Navier-Stokes equations based on primitive variables, that is, velocity and pressure, as well as velocity-vorticity algorithms. It considers both coupled, splitting, and least-squares formulations for primitive variables. Both the Uzawa coupled algorithm and a new substructured solver are discussed. The discussion on primitive variables time-splitting includes recent theoretical advances in the pressure-correction and velocity correction schemes as well as the rotational formulation of the pressure boundary condition. The final section is devoted to nonlinear terms; it includes a discussion of spatial and temporal discretization with focus on the semi-Lagrangian method for the incompressible Navier-Stokes equations.

*Keywords:*
Navier-Stokes equations, velocity, pressure, velocity-vorticity algorithms, Uzawa algorithm, substructured Stokes system, primitive variables, nonlinear terms

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