Ensemble Timestepping Algorithms for Natural Convection

TL;DR

This paper introduces two efficient ensemble timestepping algorithms for natural convection problems, enabling reliable temperature predictions and variance estimates with reduced computational costs, supported by theoretical analysis and numerical tests.

Contribution

The paper develops novel ensemble algorithms that solve coupled linear systems efficiently for natural convection, with proven stability and convergence properties.

Findings

Algorithms accurately predict temperature distributions.

Variance estimates provide reliability measures.

Numerical tests confirm theoretical stability and efficiency.

Abstract

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.