  We introduce a numerical method for extracting minimal geodesics along the
group of volume preserving maps, equipped with the L2 metric, which as observed
by Arnold solve Euler's equations of inviscid incompressible fluids. The method
relies on the generalized polar decomposition of Brenier, numerically
implemented through semi-discrete optimal transport. It is robust enough to
extract non-classical, multi-valued solutions of Euler's equations, for which
the flow dimension is higher than the domain dimension, a striking and
unavoidable consequence of this model. Our convergence results encompass this
generalized model, and our numerical experiments illustrate it for the first
time in two space dimensions.
