Reduced-Order Modeling of Stochastic Bifurcation in Naturally-Convected Flows

We present a reduced-order model to solve time-dependent stochastic thermo-fluid problems with high dimensional random initial/boundary conditions. To this end, we develop a methodology for representation and evolution of spatial and stochastic modes of a random system. The flow variables are modeled as stochastic processes represented in terms of Karhunen-Loeve modes. The modes dynamically evolve with the flow and adapt to the stochasticity which is introduced into the system by random initial or boundary conditions. We present our results for the Rayleigh Bernard Convection. We investigate the effect of stochastic initial conditions and stochastic boundary conditions on bifurcation. The computational performance and accuracy of this technique are compared with results from the polynomial chaos method.