A fluid solver based on vorticity – helical density equations with application to a natural convection in a cubic cavity

We study numerically a recently introduced formulation of incompressible Newtonian fluid equations in vorticity – helical density and velocity – Bernoulli pressure variables. Unlike most numerical methods based on vorticity equations, the current approach provides discrete solutions with mass conservation, divergencefree vorticity, and accurate kinetic energy balance in a simple and natural way. The method is applied to compute buoyancy-driven flows in a differentially heated cubical enclosure in the Boussinesq approximation for Ra ∈ {10, 10, 10}. The numerical solutions on a finer grid are of benchmark quality. The computed helical density allows quantification of the three-dimensional nature of the flow. Copyright c ⃝ 2011 John Wiley & Sons, Ltd.