Fluid models

In this section, we will detail the equations describing the hydrodynamics of Newtonian incompressible fluids. We first introduce the stationary (subsection Stationary Stokes equations) and unsteady Stokes problem (Unsteady Stokes equations), before considering the Navier-Stokes equations (Navier-Stokes equations). For each problem, we write its variational formulation, which is required to implement its numerical solution using the Feel++ library, written in C++. For the stationary Stokes problem, we describe the functions used in the implementation, and we verify it with test cases.