Multiscale numerical modeling of multiphysics systems

点击翻译按钮获取中文摘要

This project focuses on multiscale and stochastic numerical methodsfor complex multiphysics problems. A parallel computational frameworkfor modeling various multiscale applications will be developed. Themodels of interest will be based on coupling the Stokes or theNavier-Stokes equations with single phase or multiphase Darcy flow.The flow system will be coupled with reactive transport. The researchapproach is based on a multiblock domain decomposition methodology.The simulation domain is a union of subdomains (blocks). Each blockis associated with a physical, mathematical, and numericalmodel. Physically meaningful interface conditions are imposed on thediscrete level via mortar finite elements. The formulation providesgreat flexibility for multiphysics and multinumericscouplings. Furthermore, this domain decomposition approach, combinedwith coarse scale mortar elements, provides a multiscale approximationand an efficient way to solve the coarse grid problem in parallel.Uncertainty in the physical characteristics is modeled via stochasticpartial differential equations. Approximation in probability space isachieved using stochastic finite element and collocation methods. Themain components of the research will be 1) development of multiscalemathematical models, identifying appropriate interface conditions, andanalysis of the well-posedness of the models; 2) novel discretizationtechniques for stochastic partial differential equations; 3) aposteriori error estimates and adaptive mesh refinement algorithms inphysical and stochastic space; and (4) efficient parallel domaindecomposition solvers and preconditioners.The research methodology can be applied for the design, analysis, andimplementation of computational methods for a large class of problemsarising in science and engineering applications. The project willemphasize accurate, robust, and efficient numerical methods forproblems exhibiting behavior on a wide range of scales in space andtime. The research also aims to quantify uncertainty in the predictiondue to to uncertainty in the input parameters through stochasticmodeling. The research results will be applied to two mainapplication areas: couplings of surface water with groundwater flowsand modeling complex multiscale processes occurring in theinflammatory response in the human body. Computer modeling ofsubsurface and surface flow and transport has a major economic impacton environmental and energy industries. Due to the proximity ofgroundwater and surface water systems, contamination of rivers, lakes,and wetlands can lead to contamination of aquifers andvice-versa. Simulating these complex interactions is a majorcomputational challenge. Acute inflammation, which occurs in responseto trauma or infection, may lead to a systemic inflammation orsepsis. Sepsis frequently leads to organ failure and death (with morethat 500,000 fatal cases per year in the U.S.). Effective treatmentsare lacking, due to the complexity of the process. Mathematical andcomputer modeling is becoming a more common tool in the effort to gaininsight of the dynamics and spatial characteristics of theinflammatory process.