Ensemble Timestepping Algorithms for Natural Convection
For researchers in computational fluid dynamics, this provides an efficient method to quantify prediction reliability in natural convection simulations.
This paper develops two ensemble timestepping algorithms for laminar natural convection that reduce computational cost by solving coupled linear systems with shared coefficient matrices, and proves stability under a timestep condition. Numerical tests confirm the theory and demonstrate predictability horizons.
This paper presents two algorithms for calculating an ensemble of solutions to laminar natural convection problems. The ensemble average is the most likely temperature distribution and its variance gives an estimate of prediction reliability. Solutions are calculated by solving two coupled linear systems, each involving a shared coefficient matrix, for multiple right-hand sides at each timestep. Storage requirements and computational costs to solve the system are thereby reduced. Stability and convergence of the method are proven under a timestep condition involving fluctuations. A series of numerical tests, including predictability horizons, are provided which confirm the theoretical analyses and illustrate uses of ensemble simulations.