Sensitivity Analysis of Navier-Stokes Equations Coupled with Temperature Using the First-Order Polynomial Chaos Method and Fev Discretization
Abstract
This paper uses the polynomial chaos method to analyze sensitivity in heat transfer problems governed by the Navier-Stokes equations coupled with a temperature equation. The intrusive polynomial chaos method incorporates uncertain variables as combinations of orthogonal polynomials, known as polynomial chaos expansions (PCEs), directly into the governing equations. This transformation turns the original deterministic PDEs into coupled deterministic equations for the PCE coefficients. We apply first-order PCM and propose a decoupling approach for state and sensitivity systems. We discretize the state equations and their sensitivity using to the Finite Element-Volume method. We establish a stability estimate for the continuous and discrete state and sensibility equations.
