The equations of inviscid gas dynamics are systems of conservation laws, purely hyperbolic in character. The equations governing incompressible flow, by contrast, include hyperbolic equations governing advection, parabolic equations for the Crank-Nicolson discretization of diffusing quantities, and elliptic equations to enforce the velocity divergence constraint. Our treatment of the first step uses a specialized second-order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid and high Reynolds number flow. Density and other scalars are advected in such a way as to maintain conservation, if appropriate, and free-stream preservation. This simulation is an inviscid calculation of a spatially evolving turbulent plane jet.
Turbulent jets have applications in such fields as propulsion, combustion and environmental flows.
In the case of combustion, many engines are designed to have the fuel and oxidizer introduced into the combustion chamber as co-flowing jets. Mixing on the molecular level of these two streams is essential for combustion to occur. Near the inflow, the mixing process is dominated by the large-scale structures in the flow. Further downstream, as the jet develops, the mixing is influenced more by small-scale turbulence. Mpeg animations are available of the evolution of the vorticity and passive scalar fields in this jet.