The reversible contribution to contemporary theories of non-equilibrium thermodynamics is reviewed as a methodology for attacking difficult, conservative problems in complex fluid dynamics. Several examples of past successes are discussed, and a new application is addressed: non-equilibrium molecular dynamics (NEMD) simulations. NEMD simulations of fluids are generally based on either a DOLLS or SLLOD tensor algorithm. The former is always considered to be a Hamiltonian system, but not particularly useful in high strain rate flow simulations, while the latter is considered not to be a Hamiltonian system, but much more practical and accurate in flow simulations. We demonstrate herein using non-canonical transformations of the particle momenta of the system that the SLLOD equations, when written in terms of appropriate non-canonical variables, are completely Hamiltonian, whereas the DOLLS equations are not so. A modified set of DOLLS equations in terms of the non-canonical variables which again is completely Hamiltonian is also derived. Both algorithms then lead to a phase space distribution function which is canonical in both the coordinates and momenta.