Dr. Ahmed Kaffel' s research activity is best summarized as the development of novel numerical methods which are used, along with classical tools of applied mathematics, to solve physical problems of current interest in fluid mechanics and porous media. Active research interests include:

  • Inverse problem and medical imaging: Wavelet algorithms for a high-resolution image reconstruction in magnetic induction tomography.
  • Data Science, Data visualization, Machine learning
  • Computational biology: Mathematical modeling of biological and cardiovascular systems
  • Fluid Mechanics of newtonian and complex fluids: Computational fluid dynamics, Hydrodynamic stability of shear flow, dynamics in fluidized beds, turbulence models, and free surface flow.
  • Multiphase flow in porous media: Volume averaging approach, Modeling unsaturated flow of a liquid through multiple layers of thin, swelling porous media
  • Partial and ordinary differential equations: Nonlinear dynamics and chaos, optimal control and dynamical system.
  • Numerical analysis and scientific computing
  • Numerical solutions of PDEs using:

    • Finite element and Discontinuous Galerkin methods
    • Spectral methods
    • Finite volume method
    • Finite difference essentially non-oscillatory (ENO) methods and weighted ENO (WENO) methods
    • Boundary element method and ALE method

He developed efficient numerical solvers using higher order numerical methods (such as Finite Volume Method (FVM), Finite Element Method (FEM), Finite Difference Method (FDM), Finite difference essentially non-oscillatory (ENO) methods and weighted ENO (WENO) methods, Spectral Method, and Boundary Element Method (BEM)...) to solve complex system of differential equations and favor finding analytical solutions to simplified problems whenever possible.

He illustrated the importance of fluid dynamics and porous media research by considering particular areas of study including waves and instabilities in microchannels, hydrodynamics stability of shear flow instabilities for newtonian and viscoelastic fluids, stability and multiphase flow in porous media, turbulence and environmental free surface flows, instabilities and dynamics in fluidized beds, potential flow and flow control. Recently, he started working on new topics including inverse problems, machine learning, and their applications to biomedical and health care problems. Some of his recent research work including inverse problem, medical imaging, porous media and fluid mechanics are described below: