Hyperbolic systems with periodic boundary conditions: An example with Euler equations (Q1060916)

Hyperbolic systems with periodic boundary conditions appear to be a challenge to the numerical analyst. In this paper, the Euler equations of incompressible fluid dynamics are analyzed - from the computational point of view - in the stationary, periodic, two and three dimensional cases. We show that the usual methods for solution of hyperbolic problems are not well suited. The problem is solved by least squares; existence and uniqueness are discussed and some numerical results are shown for a problem arising in turbulence modelling.