Multiscale Modeling and Simulations
In many areas of science and engineering, we face the problem that we are interested in analyzing the macroscale behavior of a given system, but we do not have an explicit and accurate macroscopic model for the macroscale quantities that we are interested in. On the other hand, we have a microscopic model with satisfactory accuracy (e.g. a molecular dynamics model)- the difficulty being that solving the full microscopic model is far too inefficient. Therefore it is desirable to develop hybrid numerical methods that are based on a combination of the two formulations in order to take an advantage of both the efficiency of the macroscale model and the accuracy of the microscale model.
Coupled atomistic-continuum methods. My work in this area includes: (1) the development of coupled atomistic-continuum methods for fluids (including problems with unknown constitutive equation and/or unknown boundary conditions) in the framework of the heterogeneous multiscale method (HMM); (2) the stability analysis of domain-decomposition type of multiscale methods, and (3) the development of a general scheme for designing seamless multiscale methods. See the following references for more details.
- A general strategy for designing seamless multiscale methods,
W. E, W. Ren and E. Vanden-Eijnden, J. Comput. Phys. 228, 5437 (2009)
- Sequential multiscale modeling using sparse representation, C. Garcia-Cervera, W. Ren, J. Lu and W. E, Commun. Comput. Phys. 4, 1025 (2008)
- Seamless multiscale modeling of complex fluids using fiber bundle dynamics, W. Ren, Commun. Math. Sci. 5, 1027 (2007)
- Analytical and numerical study of coupled atomistic-continuum methods for fluids, W. Ren, J. Comput. Phys. 227, 1353 (2007)
- Heterogeneous multiscale methods: A review, W. E, B. Engquist, X. Li, W. Ren and E. Vanden-Eijnden, Commun. Comput. Phys. 2, 367 (2007)
- Heterogeneous multiscale method for the modeling of complex fluids and micro fluidics, W. Ren and W. E, J. Comput. Phys. 204, 1 (2005)
- A General framework for designing seamless multiscale methods , W. E, W. Ren and E. Vanden-Eijnden, preprint
- Sequential multiscale modeling using sparse representation, C. Garcia-Cervera, W. Ren, J. Lu and W. E, Commun. Comput. Phys. 4, 1025 (2008)
The moving contact line problem. When two immiscible fluids are placed on a substrate, the line where the interface of the two fluids intersects the solid substrate is called the contact line. The equilibrium configuration of the static contact line is described by the Young's relation which relates the three coefficients of interfacial tension to the contact angle formed by the fluid-fluid interface with the solid surface. The moving contact line problem, however, has for many years remained an issue of controversy and debate. The main difficulty stems from the fact that classical hydrodynamic equations coupled with the conventional no-slip boundary condition predicts a singularity for the stress that results in a non-physical divergence for the energy dissipation rate. Recently, we systematically investigated the physical processes and various forces near a moving contact line using molecular dynamics. Based on this study we formulated a sharp-interface continuum model for the moving contact line problem.
- Contact line dynamics on heterogeneous surfaces, W. Ren and W. E, Phys. Fluids, 23, 072103 (2011)
- Continuum models for the contact line problem,
W. Ren, D. Hu and W. E, Phys. Fluids, 22, 102103 (2010)
- Derivation of continuum models for the moving contact line problem based on thermodynamic principles,
W. Ren and W. E, Commun. Math. Sci. 9, 597 (2011)
- Boundary conditions for the moving contact line problem,
W. Ren and W. E, Phys. Fluids, 19, 022101 (2007)
WEIQING REN Last modified: Mon Dec 3 20:55:34 EST 2007