Computational Continuum Mechanics is about numerical study of physical phenomena where continuum applies. When the length and time scales characterizing the physical phenomenon are very large compared to the molecular length and time scales, the continuum hypothesis enables representation of the physical laws governing the conservation of mass, momentum, energy and charge in the form of systems of coupled partial differential equations.
This allows us to study, by numerically solving these equations, a wide spectrum of applications, ranging from blood flow in our capillaries to oceanic and atmospheric flows from the human scale up to the planetary scale. The numerical tools vary from grid-based such as finite element, finite volume and finite difference methods to grid-free Lagrangian particle methods such as Vortex Methods. These numerical frameworks allow us to use computational mechanics to optimize the shape of an airplane to minimize drag, to predict future weather, and to design lab on-chip and micro-total analysis micro-devices, to name a few. In addition, advancing further the state of the art of these numerical methods enables us to tackle more challenging problems that incorporate complex physics in multiple domains.
Prof. Issam Lakkis (MSFEA)
- 3D Vortex Methods: fast solvers, grid-free schemes for diffusion, accurate modeling for the vortex stretching and tiling terms in regularized vortex methods, and enforcing the divergence-free condition on the vorticity vector field.
- Lagrangian Transport in stochastic flow fields with application to pollution transport in the atmosphere and ocean (Mediterranean and Red Seas) [In collaboration with researchers at KAUST].
- Source reconstruction using Bayesian Inferencing frameworks with application to pollution transport in the atmosphere and ocean (Mediterranean and Red Seas) [In collaboration with researchers at KAUST].
- Analysis, modeling and design of 2D and 3D micro-channel flows, microfluidic transistors and mixers, and energy harvesting micro-devices.
- Multi-scale Gases transport in the airways up to exchange with the blood in the capillaries circulating the alveoli [In collaboration with Researchers at Stanford University]