Multi-scale description of multi-phase fluid flows using data-driven closures

点击翻译按钮获取中文摘要

An accurate description of multi-phase fluid flows that is accompanied with an efficient numerical method remains one of the challenges in the realm of scientific computing. The target of this research proposal is to devise a continuum model that deploys data-driven mesoscale closures based on underlying molecular interactions. In particular, considering moment equations resulting from the Enskog-Vlasov kinetic equation, the unclosed terms in the conservation laws can be modeled using the moments of conserved quantities and their spatial derivatives. Once an appropriate basis function for solution space is utilized, the closure problem converts to a regression problem of finding the projected coefficients for terms associated with molecular interactions given the moments around the point of interest. Here, an efficient high dimensional regression model from Machine Learning literature such as Artificial Neural Network suitable for the closure problem will be deployed and trained offline. The training data set will be generated by performing Monte Carlo mesoscale simulations in a reference configuration for an applicable range of boundary conditions. Finally, as the target test case, the trained multi-scale solution algorithm will be tested by studying the evolution of Stratospheric aerosols in a relevant simulation setting. As the outcome, this research proposal intends to provide an efficient, accurate, and flexible framework for large scale simulations of fluid flows that allows consistent inclusion of micro-scale physics in the classical conservation laws using efficient high dimensional regression methods.The applicant has chosen Prof. Nicolas G. Hadjiconstantinou at Massachusetts Institute of Technology (MIT) to be the host for this postdoctoral study, because of his extensive research and relevant contributions for variance-reduction Monte Carlo methods in kinetic theory as well as multi-scale modeling. Furthermore, Prof. Youssef Marzouk at MIT, who is an expert in Bayesian inference and uncertainty quantification, will support the applicant with devising a reliable regression model relevant for this research proposal.