Northwest Consortium for Multiscale Mathematics and Application
EMSL Project ID
32299
Abstract
This project is funded by Department of Energy (DOE), Advanced Scientific Computing Research (ASCR) program. The mission of this project is to build up the mathematical foundation for upscaling and computational coarsening, bridge the length- and time-scale gap between fine-scale and coarse-scale models and apply the new multicale model for reactive transport, fuel cell research, subsurface modeling and carbon geological sequestration, which is relevant to EMSLs mission and one of the four EMSLs science themes: Science of interfacial phenomena science theme. We are looking forward to employ the computational resources at EMSL to utilize the new multiscale tools to solve the large scale grand challenge problems.The complexity in many microfluidic and biomedical applications facing the DOE requires the development of new multiscale capabilities to model accurately multiscale flow phenomena across several orders of magnitude in space and time scales. Multiple scale model in both time and space can overcome this difficulty and provide a unified description of liquid flows from nanoscale to larger scales. We propose a new multiple particle formalism based upon hybrid pore-scale model, which couples the fine fundamental particle, coarsened particles derived from the fine scale, and, the continuum. An example of the proposed coupled approaches is the combination of atomistic dynamics, dissipative particle dynamics (DPD), and the incompressible Navier-Stokes equations.
Another way to bridge different scales is to use probabilistic closure. We propose a new stochastic meso-scale model based on Lagrangean particle solution of coupled Langevin, continuity, and advection-diffusion equation. The novel part of the research will be the strict derivation of the stochastic mesoscopic Langevin-type PDEs from the underlying micro-scale system of ODEs, and the development of Lagrangean particle solution of the system of stochastic PDEs. This model will allow advective mixing and the diffusive mixing to be treated separately. Advective mixing will result from random correlated motion of liquid particles, whose trajectories will be found from solution of Langevin and continuity equation, while diffusion will be governed by the diffusion equation. Additionally, we are developing stochastic hybrid dynamics software, which expands the capability of STOMP to be able to model heterogeneous porous media and link the Darcy scale and pore scale together by building a stochastic interface between pore-scale Navier-Stokes solver Nektar and Darcy scale simulator STOMP.
The proposed work will have significant and broad impact as it will contribute towards a rigorous foundation for upscaling and computational coarsening. It will establish a new multiscale model in systems of great interest to DOE that goes across several scales. Thus, the new approach will improve our capability to simulate complex multiscale systems that we can address.
Project Details
Project type
Exploratory Research
Start Date
2009-01-12
End Date
2010-01-17
Status
Closed
Released Data Link
Team
Principal Investigator
Team Members
Related Publications
Lin G, and AM Tartakovsky. 2009. "An efficient, high-order probabilistic collocation method on sparse grids for three-dimensional flow and solute transport in randomly heterogeneous porous media." Advances in Water Resources 32(5 SP ISS):712-722.
Wang-yi Wu and Guang Lin. "Basic function scheme of polynomial type." Applied Mathematics and Mechanics, 2009, Volume 30, Number 9, Pages 1091-1103. DOI: 10.1007/s10483-009-0903-y
Zhiliang Xu, Guang Lin. "Spectral/HP element method with hierarchical reconstruction for solving nonlinear hyperbolic conservation laws". Acta Mathematica Scientia, Volume 29, Issue 6, November 2009, Pages 1737-1748