Stochastic Model Reduction of Allen-Cahn Phase Field Model with High Dimensional Random ForcingtextBajpayi, MayankcreatorKarniadakis, GeorgeAdvisorBrown University. School of Engineeringsponsor20175, 40 p.born digitalThesis (Sc. M.)--Brown University, 2017thesesThe Karhunen-Loeve (KL) decomposition provides a low dimensional representation for square integrable stochastic fields as it is optimal in the mean square sense. Despite the success of these methods for many stochastic systems of practical interest, potential roadblock occurs in strongly time-dependent problems. Motivated by this limitation, Sapsis and Lermusiaux(2009), developed the dynamically orthogonal(DO) framework, which allows for the simultaneous evolution of both the spatial basis and stochastic basis. Using the framework of Dynamical Orthogonality(DO) condition, a coupled set of evolution equations are derived for Allen-Cahn phase field transport equation. The reduced order field equations (DO equations) consists of (i) the system of Partial Differential equations(PDEs) that describes the evolution of the mean field and the orthonormal spatial basis(modes) defining the stochastic subspace where uncertainty "lives" and (ii) the set of Stochastic Differential equations(SDEs) that describes the evolution of stochastic basis(coefficients) defining how the stochasticity will be evolved within the reduced order stochastic subspace. Numerical simulations are performed for time independent high dimensional stochastic forcing based on Karhunen-Loeve(KL) decomposition. The aim of the current work is to investigate dimension reduction in high dimensional random space by analyzing the number of DO modes required to resolve the transient stochastic Allen-Cahn equation.Numerical analysisEnglishRPB2017061610.7301/Z05X27B2In CopyrightCollection is open for research.