ABSTRACT
This chapter considers a Lagrangian approach to derive the expression for the internal energy density. In spherically symmetric Lagrangian mass coordinates the role of the continuity equation can be served by an expression that traces the radial position of a mass shell. Even though a Lagrangian formalism was intended to shift the emphasis from grid coordinates towards fluid parcel trajectories, in practice they still expressed the conservation laws in terms of spatial coordinates. Whereas the Eulerian form is written with a fixed grid in mind, the Lagrangian form suggests Lagrangian coordinates where the grid moves with the fluid elements. These different ways of thinking about the grid suggest different algorithmic approaches to numerically solving the equations of fluid dynamics in computer simulations and either approach has its pros and cons. The chapter formulates the pressure in terms of a net momentum transfer across fluid parcel boundaries, carried by individual constituent particles.
