Intermittent behaviour in hydrodynamical systems with spherical symmetry: theory and an experiment

Auxiliary variable methods for the incompressible Navier-Stokes equations approximate the evolution of the velocity through a dynamic variable which does not satisfy a divergence constraint but from which the correct incompressible velocity can be computed by a projection. This approach is a departure from traditional projection methods wherein the intermediate variable is considered only as a byproduct of a fractional step scheme. I will discuss the connections between auxiliary variables, impulse variables, and projection methods; discuss how auxiliary variables resolve the question of applying boundary conditions in projection methods; and discuss recent work on constructing fourth-order methods for the equations of 0-Mach number gas dynamics based on auxiliary variables.