Investigation of Entropy in Numerical Simulations of Euler Equations

The Euler equations are a set of hyperbolic partial differential equations that describe the conservation of (usually) internal energy, density, and velocity of a moving, ideal fluid. Ideal here means inviscid and non-heat conducting. With the evolution of these three independent state variables, the full state of the fluid can be constructed. A state variable of interest is the entropy of the fluid. While theoretically entropy can be used in place of another state variable in numerical simulations, the evolution of entropy is governed by a partial differential inequality rather than an equality assuming the fluid is ideal. This work investigates how entropy behaves and evolves theoretically and numerically.