Discrete Hamilton's equations for viscous compressible fluid dynamics

Lagrange’s and Hamilton’s equations are used extensively in numerical modeling of rigid body dynamics and continuum solid dynamics problems. The use of energy methods in viscous compressible flow problems has been by contrast rather limited, largely confined to the development of basic balance laws in partial differential equation form. However, finite element interpolation of the modeled flow field allows for the direct application of the discrete form of Hamilton’s equations to viscous compressible fluid dynamics in Eulerian frames. The resulting model is a true energy formulation, developed without reference to the partial differential balance equations which underlie conventional finite difference, weighted residual finite element, and finite volume methods.