A Stochastic Multiscale Computational Framework for Multiphysics Systems

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The primary objective of this project is to develop a stochastic multiscale computational framework for modeling multiphysics systems arising in science and engineering applications with multiscale and uncertain input parameters. The mathematical models involve transient Stokes-Darcy systems coupled with systems of reaction-advection-diffusion equations. A multiblock domain decomposition methodology provides robust and efficient multiphysics and multinumerics couplings. The simulation domain is decomposed into a union of subdomains, each one associated with a physical, mathematical, and numerical model. Physically consistent interface conditions are imposed using mortar finite elements. Coarse scale mortar spaces lead to efficient and accurate multiscale approximations. Stochastic partial differential equations are employed to model uncertainty in the physical parameters. Sparse collocation methods are used for approximations in probability space. The project will investigate 1) mathematically rigorous and physically meaningful multiphysics models; 2) robust, accurate and efficient multiscale physical space and stochastic space discretization techniques; 3) a posteriori error estimates for adapting the models, the numerical grids in physical space, and the set of collocation points in stochastic space; 4) multiscale stochastic-based data assimilation and parameter estimation algorithms; 5) multiscale parallel domain decomposition solvers and preconditioners.The work will emphasize computational modeling of energy and environment applications, in particular coupling of surface water with groundwater in hydrological systems, as well as biomedical applications such as modeling the inflammatory response in the human body. Both types of systems involve complex interactions of different physical processes and exhibit variability and uncertainty in the input parameters on a wide range of spatial and temporal scales. Computational modeling of coupled subsurface and surface flows and transport can provide reliable and cost effective predictions in contaminant remediation of rivers, lakes, wetlands, and aquifers. Inflammation plays a major role in the response of the human body to trauma, infection, or various diseases. Mathematical and computational modeling of these very complex processes can provide better understanding of their dynamics and spatial characteristics and may lead to the design of more effective treatments.