A wave equation approach to the numerical solution of the Navier-Stokes equations for incompressible viscous flow

In this Note we describe a novel method for the solution of the Navier-Stokes equations for incompressible viscous fluids. This method, which can be viewed as an alternative to the methods of characteristics, takes advantage of a time discretization by operator splitting to decouple incompressibility-diffusion from advection. The incompressibility-diffusion steps can be treated by classical Stokes solvers. Concerning the advection steps, thanks to the incompressibility of the advecting field, we can replace the corresponding transport equations by second order in time wave equations, which are much easier to solve numerically despite the fact that they are associated to degenerate elliptic operators. Numerical experiments confirm the good computational properties of the new method.