A combinatorial algorithm for the euler equations of incompressible flows

Abstract

A Lagrangian time discretization is introduced for the Euler equations of inviscid incompressible flows, using the least square projection onto the manifold of volume preserving diffeomorphisms. A further discretization is performed first by splitting the physical domain into N blocks of equal volume, then by approximating each volume-preserving mapping involved in the time discretization by a permutation of the N blocks. Finally, a combinatorial algorithm is obtained, where the classical assignment problem has to be solved at each time step.