Accurateand Robustmethods for Variabledensity Incompressible Flows with Discontinuities

We are interested in the solution of incompressible ows possessing densities that vary both discontinuously and smoothly. Smooth density variations might be caused by temperature eeects, whereas abrupt variations are present at immiscible uid interfaces. If interfaces are present, we wish to model their gross topological changes. The design of an incom-pressible ow algorithm that maintains solution accuracy and simulation robustness in the presence of density variations presents challenges, especially if the variations are discontinuous and topologically complex. We discuss the construction of robust, high-delity fractional-step projection methods for computing such ows. We focus on algorithms for the projection, the numerical linear algebra, and interfacial physics such as surface tension. Also discussed are algorithms for multi-dimensional advection and volume tracking. Numerical examples are presented to illustrate our current capabilities.