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, divergence‐free 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 cubic enclosure in the Boussinesq approximation for Ra ∈ {10⁴,10⁵,10⁶}. 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 © 2011 John Wiley & Sons, Ltd.