Combination of Karhunen-Lo`eve and intrusive polynomial chaos for uncertainty quantification of thermomagnetic convection problem with stochastic boundary condition

Uncertainty propagation analysis plays a crucial role in understanding the impact of variations in initial condition, boundary condition, and fluid physical properties on simulation results for thermomagnetic convection heat transfer problems. To effectively analyze the uncertainty problem of thermomagnetic convection caused by random temperature fluctuations, a novel and comprehensive computational framework based on intrusive polynomial chaos approach was proposed in this paper. Our proposed approach aims to represent random temperature boundaries using Karhunen-Loe`ve expansion (KLE) and stochastic output response using polynomial chaos expansion (PCE). In addition, we use spectral projection method to transform the stochastic control equation into a group of deterministic control equations. We obtained the uncertainty characteristics of the stochastic output response by solving each polynomial chaos basis. Compared with Monte Carlo simulation (MCS), our approach accurately and efficiently predicts the uncertainty characteristics of thermomagnetic convection problems under stochastic temperature boundary conditions while significantly reducing computational resources.