Hyperbolic systems with periodic boundary conditions: An example with Euler equations

AbstractHyperbolic 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