A DGFEM discretization has been developed for the Hamiltonian dynamics of stratified incompressible linear fluid flow. The developed discretization can handle the numerical challenges posed by wave attractors: the three dimensionality of the domain, the focusing of wave energy and the incompressibility of the flow. The discretization is unconditionally stable. The conservation of phase space and energy ensure that the numerical error is physically more correct since an unphysical numerical error that changes the total energy is not possible.