A Second Order Ensemble Timestepping Algorithm for Natural Convection
Joseph Anthony Fiordilino · SIAM Journal on Numerical Analysis · 2018
This paper presents a second-order accurate algorithm for calculating an ensemble of solutions to natural convection problems. Solutions are calculated by solving two uncoupled linear systems, each involving a shared coefficient matrix, for multiple right-hand sides at each timestep. Storage requirements and solution time are reduced. Stability and second-order accuracy of the method are proven under a CFL-type condition involving fluctuations of the velocity. Numerical tests are presented which confirm the theoretical analyses.